Transcript for:
Mathematics and Financial Concepts Breakdown

[Music] yes uh very good evening everyone yes so uh we are done with uh logical reasoning so we'll start with the new section that is mathematics right so i said that calculation is very very important so once again we'll be doing that for a couple of minutes so that once you get what clarity in that you can proceed on to the subject so because this is uh this is very important for maths as well as statistics very very important because otherwise you'll waste a lot of time doing the calculation itself right so let us start with the calculation so ready with the calculators everyone yeah right so i think i have given you the syllabus right mathematics how many of you have no syllabus with you i mean you do three right okay you have a syllabus with you okay so quickly i shall just give you the syllabus first then i'll take you through the calculations all right yes uh let's get back so there are how many chapters in maths eight chapters so the weightage of mathematics is 40 marks objective or subjective objective right so first chapter ratio proportion in the indices logarithm what's the weightage of the chapter four to five marks second chapter equations the weightage of this chapter is 3 to 4 marks chapter number 3 linear inequalities the weightage is only one two two chapter number four time value of money 12 to 16 questions would come from this chapter alone right chapter number five permutation and combination the weightage of this chapter is three to four chapter number six is sequence and series the weightage of this chapter is three to four again chapter number seven sets relations and functions so again three to four the last chapter is differential and integral calculus the weightage of this chapter is four to five marks so these are the eight chapters that we will be covering under max so as you can see the weightage of which chapter is more time value of money time value of money it takes more time not to solve the questions to cover the syllabus to solve the questions 10 to 15 seconds maximum 30 to 40 seconds not more than that you will know right so if you solve it conventionally yes two two minutes time two to three minutes time is required to solve a question so we are not going to solve in a conventional method yes i am going to solve uh the question in a conventional method first then i'll give you the shortcut you will understand the difference right okay so this is the syllabus of mathematics okay as i said the calculation is the key the calculation is the key all right so let's begin with a calculation what calculation am i talking about it's a memory calculation maths paper is objective it's not subjective paper three is object to complete paper three is objective a question will have four option every correct answer that you take you get one mark or wrong answer minus zero point two five right it's objective there are two objective papers what are those paper 3 math stats logical reasoning and paper 4 economics and bck that paper and paper 3 and paper 4 are objective paper one and paper two are subjective all right okay so memory calculation so what's the importance of memory calculation is listen suppose if you want to do calculation like 25 into 43 minus 48 into 9 19 okay plus 65 into 23 minus 18 into 37 so you'll how you you'll actually carry out the calculation you will type 25 into 43 write down the value minus 48 into 19 you'll write down the value then 65 into 23 you will write down the value again then 18 into 37 you would write down the value then what you do you feed these values in the calculator can you tell me these values quickly 25 into 43 thousand seventy five forty eight into nineteen nine twelve sixty five into twenty three how much thousand four nine five eighteen into thirty seven 6 6 6. now what do you do you feed these values in the calculator tell me the final answer 9 92 so this is the value right but if you write all this you're spending a lot of time on this right so you're not going to do this in the exam instead what do you do you first feed the values whatever within the brackets 25 into 43 feed the value first now if you type 25 into 43 you get a result that result is not supposed to be written on the paper rather you will store that value in the calculator itself so how do you do that after 25 into 43 see what is there without outside the brackets to the left of the brackets what do you have there is nothing there is nothing means it's a positive value so to store that you press a button m plus so what is m plus by pressing m plus the value whatever you typed so far that gets stored in the memory as positive value now after storing this value you are not supposed to press negative button what you need to type whatever within the brackets so type 48 into 19 and look at the sign before the brackets it's negative so what do you press now m minus then what do you do do you press a positive button no whatever within the brackets that is 65 into 23 what do you press now m plus next 18 into 37 press what m y m minus because it's a negative value finally you're going to recall the value from the memory for that press m rc by m by the moment you press mrc whatever values that you kept kept on storing that will be recalled from the memory so mrc basically means what memory recall so what's the result isn't it 992 same answer so you need not write this step at all every calculation i mean especially memory calculations i mean the calculation should be used been done using what memory of your calculator otherwise it will take a lot of time you will be spending a lot of time in the calculation itself am i clear am i clear so you understood when to use m plus whenever you want to store the value in the memory as a positive value m plus and if you want to store the value as a negative in the calculator m minus how do you recall a value from the memory mrc so are these points clear so far are these points clear so far everyone online students yes okay shall we move on shall we move on okay okay sometimes you may come across the calculation say 1 by 5 into 2 by 6 minus 2 by 8 into 4 by 7 plus 6 by 9 or 6 by 7 say 6 by 7 into 1 by 3 so how do you carry out the calculation so you will have to do 2 1 into 2 is 2 divided by 5 into 6 is 32 by 30 then two fours are eight eight by 56 then six ones are six divided by seven threes are 21 it'll take a lot of time if you do that so what you do tell me what is that i said to feed in the calculator first whatever within the brackets so type one by five first type one by five then there is a multiplication right pressure into button please do the calculation into what two divided by six as it is you type one by five into two by six now look at the sign before the bracket positive what do you press m plus what do you do next same thing 2 by 8 into what 4 by 7 2 by 8 into 4 by 7 press what m minus 6 by 7 into 1 by 3 press what m plus finally mrc so what is the value 2095 is that the answer everyone got is that the answer everyone got online students please do respond is that the answer yes i want everyone to respond guys yes so nice clear so far is it clear so far understanding right okay please feed the values in the calculator okay don't just copy whatever i'm writing over here more than that what has been done that has to be practiced in the calculator if you don't practice the speed will not come the speed will not be improved unless you practice right so please do feed the values right so is it clear so far and nothing to be buy hearted here right is it required to buy out anything just follow the basics what is it whatever within the bracket has to be typed first clear okay shall we move on shall we everyone guys have you all got this answer got it please do tell me if you haven't got the answer have you all got the answers yes shall we shall we move on memory if there is a memory issue you have to clear it so better you have bought the other character use that only i think that is having that is not having any issues right yeah guys let's move on to the next uh calculation normally you come across summation x into x minus y or x plus y right so where do you come across such calculation in statistics statistical problems or summation x into y summation x minus y the whole square these kind of expressions where you see in statistics okay so i'll give you a note first of all before moving forward guys if you want to raise the power of any value to raise the power of any number to n what is n the power okay then what are you supposed to do type the number type the number press what press into and keep pressing equal keep pressing equal until what until the counter number is how much counter number is n plus 1 so what is the meaning of this say for example you want to find three power six okay what is n here six the the number is 3 3 power 6 you need to find conventionally what is the meaning of 3 power 6 3 into 3 into 3 into 3 into 3 into 3 exam will get over if you do all this like this especially in mathematics and time value of money chapter itself sometimes you may have to raise the power to 36 what do you do in that case so it will take a lot of time so instead of doing this way what you can do type the number what is the number here three then what type the number after that press into then what keep pressing equal until what look at the display on the display you you if you press equal to button uh the display counter will show number right on the top of the display so what is the number it shows after pressing equal to it shows three right first when you press equal to once it will show three okay that is the counter number okay you have to keep on pressing equal until what the counter number is one more than this actual power that means it should be seven so what is the value 7 29 isn't it 729 similarly can you find out for 2 power 12 quickly 4 000 96 so have you understood how to raise the power of a number so what should be the counter number one more than actual power right is it clear everyone calculations is the key guys okay shall we move on shall we okay so let's say you have set of x values and y values say x values are 25 32 46 y values are 36 47 and 62 okay these are x values and y values uh as i said you will come across expressions like summation x into y summation x into x plus y summation x into x minus y let's say summation x minus y the whole square this kind of expression that you will come across normally in statistics okay now how to carry out the calculation nice whenever you have an expression within the summation you have to see what is that x and y they are separated by nothing that means multiplication so you need to do x into y each x and y values have to be multiplied then for summation what you need to do you have to add them together guys otherwise how do you do it conventionally each x into y 25 into 36 you'll write down the value 32 into 47 you'll write down the value 46 into 62 you'll write down the value then you feed those value in the calculator to get the final answer okay it will take a lot of time so what you do instead summation x into y should be carried out in one step how do you do that first of all 25 into 36 that is the first set of x and y what do you do to store the value look at the sign before x it's positive right look at the sign before this first variable x it's positive so how do you store it by pressing m plus x into y m plus then what 32 into 47 press what m plus then 46 into 62 press what m plus finally mrc what is the result two thousand four not four five thousand five thousand 5256 is that the value guys i want everyone to respond please check with the calculations 5256 yes please do it you don't have calculator you yeah you have no you're practicing now okay okay not able to see it is it clear guys any doubt with this calculation please do let me know everyone got it yeah okay shall we move on to the next expression summation x into x plus y guys according to priority what is the first thing that you should type whatever within the bracket so what is that we have first x plus y x plus y means 25 plus 36 after brackets would you store the value straight away there's something right after bracket there's something what is that into x right press into button and the first value of x is 25 yeah what do you press m plus because it's a positive value continue doing the same thing for rest of the values 32 in 32 plus 47 because x plus y is 32 plus 47 into what x that is 32 press what m plus because it's a positive value 46 into 46 plus 62 into what 46 m plus mrc the result of the second expression nine thousand twenty one nine zero two one is that the answer everyone okay now let's move on to the third expression what is the third expression x into x minus y what is the first thing that you would type tell me x whatever within the bracket so 25 minus 36 into what into 25 press what m plus guys x minus y irrespective of the value x minus y could be negative or positive you what you have to see is before this x positive means press n plus if it is negative then press m minus you have to see the sign of the first variable right first x minus y that means 25 minus 36 then into what this x that is 25 then what do you do press m plus for summation clear then 32 minus 47 into what 32 press m plus next 46 minus 62 into 46 m plus mrc the answer for this minus 1491 guys do respond if you haven't got the same answer something else please tell me minus 1491 yes summation x minus y the whole square now tell me what do you first of all type x minus y then would you press m straight away you need to square it how do you square it press into press equal to if you press into equal to the value gets square right so x minus y that is 25 minus 36 what do you press into equal to y into equal to because this value has to be square what do you do after that store it by pressing m plus all right next 32 minus 47 what do you do into equal to for squaring then m plus for storing right 47 minus 62 sorry 46 minus 62 into equal to for squaring m plus for storing finally what you do mrc the answer 6 not 2. one last expression guys for the same example summation x into sorry y into this time y into y minus x the whole square now tell me the first step if you get the first step right you will you can do the rest of things what is the first thing you need to do within the bracket that is y minus x after that what do you do why it has got a square then what do you do into y then what you do m plus to store the value keep doing the same thing for other set of x and y then finally press mrc the answer for the fifth one how much is it guys please check is it 30 0803 yes guys comfortable so far with the calculations clear any doubts no doubts okay all right let's move on to next level of calculation okay suppose if you have 11 11 256 in the numerator and denominator 15.26 17.87 what do you do normally you separately divide multiply denominator terms then you divide right but it is not required to be done in that way what do you do instead type 11 256 first 11 256 first divided by the first term which is 15.26 then thinking that there is a multiplication sign here don't multiply why because the 17.87 is in denominator if it is in denominator you need to always divide especially when you have two term two terms or three terms separated by multiplication sign in between in the denominator divide them separately you need not do what 15 into 26 into 17 into 87 separately then divide nice uh so what do you do 11 256 by 15.26 what do you do after that again divide 17.87 the result of this is 41.276 otherwise what you'll be doing multiply 15.26 into 17.87 then write down the next step then divide it'll take more time right is it clear how to go about this calculation okay the next calculation say you have 25875 in the numerator and in denominator 11.25 plus 13.57 the whole square guys listen unlike the previous one you can't do the same thing here why because you have plus sign in between you got what plus sign in between so what you need to do please listen to me tell me which is the complicated expression amongst the numerator and denominator denominator is a complicated expression so guys listen to me carefully you are not going to write anything on the paper everything you are carrying out in the calculator itself so how do we do it first of all feed the complicated expression that means solve the denominator first i mean to say 11.25 type it plus 13.57 so this has to be squared how do you square into equal to now would you write that value no you can store it right positive or negative value it is positive what do you do press m the value gets stored now ultimately what you need to do numerator by denominator what's the numerator 25875 type it divided by what the denominator guys denominator is already there in the memory how do you recall mrc so eight seventy 25875 pressure divided by button and what you need to divide the denominator where's the denominator in the memory how do you recall mrc don't forget to press equal to after mrc and what is the answer 40 002 approximately 42 right 42 is the result have you understood everyone online students please do respond 41.276 oh 42 the previous answer is 42. sorry previous answer is 41.276 guys have you all understood explain again listen tell me which is the complicated expression in the given uh i mean given expression numerator by denominator out of numerator and denominator you have you can clearly see that denominator is the most complicated compared to the numerator that you will finish it off that you solve it first i mean to say 11.25 plus 13.57 type it as it is then the value has to be squared because whole square is there how do you square press into press equal to so this value in the denominator will be solved by doing so now would you write that value no if you want to keep that value in the calculator only what you do press m plus the value gets stored now ultimately what you need to do numerator by denominator what's the numerator 25875 then you need to divide right divide what denominator denominator expression is already been solved and where it is kept in the memory how do you recall mrc and after mrc don't forget to press equal to and what is the result 42.00 so approximately 42. is that clear 42.002 right shall we move on nice let's say you have 15725 and denominator is 11.37 the whole cube okay now would you use memory to this don't use memory because denominator has got only one term let me explain how to carry out this calculation in one step in the calculator guys first of all fifteen thousand seven twenty five in the numerator right type it fifteen thousand seven twenty five you type it press it divide by button okay now you got only one term in the denominator that has to be cubed right eleven point three seven you type eleven point 11.37 so literally whole cube is that you'll have to divide that by how many times three times you have to divide instead of doing it press equal to so many times you will get the answer that means what is the power here three right power is three so after dividing by 11.37 press equal to how many times from whatever is the power here so many times you press equal to same answer 10.69 you understood is it clear so if there is a whole cube for a single term if there's a whole cube for a single term then don't use a memory if there is a whole cube for addition of two terms or subtraction of two terms then you use a memory for solve the denominator store it then numerator by mrc equal to you do if there is a single term within the brackets then always just divide it by once then press equal to how many times how many ever is in the power right if the power is three press equal to so many number of times the power is four press equal to so many number of times is it clear can you do one more let us check i say you have a 586 in the numerator 2.75 whole power 6 in the denominator tell me what is the procedure 1.35 four eight so what do you do you type the numerator 586 press divided by then what 2.75 once equal to how many times six times because power is six don't keep an eye on the counter now don't ever keep an eye on the counter because already you have type 586 divided by by the time you type all this the counter number would be raised okay so you can't keep an eye on the counter keep a count on number of equal to you press if the whole power is six press equal to six times the whole power is three press equal to three times is that clear guys is that clear everyone got it are we clear so far are we clear so far okay shall we move on one last expression yes see you have to deal with uh let's say you need to find let's say 25786 on the left hand side and 12.75 plus 16.58 the whole square into x so solve for x so normally what you do if you want to solve for x you return x on one side send everything else on the other side tell me if you retain x on the right hand side this expression should go where to the denominator of the left hand side first of all this has to be solved first it's a complicated expression yeah it has to be solved first how do you solve this 12.75 plus 80 16.58 how do you square that into equal to the value got squared what do you do with that would you write the value no what do you do instead store it by pressing what m plus now this value would go where to the denominator of left hand side so you type what 25786 would you multiply or divide divide because this value only will go to the denominator of lhs so why we are dividing by what value this value only where is this value in the memory how do you recall that by pressing mrc don't forget to press equal to what is the result 29.975 very often you'll get to do such calculations okay so don't write the values like 25 000 786 then the addition of 12.75 plus 16.58 is how much 29 point something into x then divide will take lot of time okay so hope you understood this calculation right everyone guys are we clear so far please tell me is there any issue are we clear with the calculation so the speed has to improve definitely i'll make you practice a lot okay well it's following problems problems only you will get the speed okay but you must know what to do when if you want to store the value in the memory as a positive you press what m plus before that you need to do something what is it feed the value right then to store the value in the memory as a negative value you press a minus to recall the value from the memory mrc now priority is always given for what whatever within the brackets after the brackets if there is a multiplication and also there is a plus or minus which one would you give the priority to multiplication after the brackets you solve then the next priority goes to multiplication or division then comes the priority to what addition or subtraction please do remember the priorities first whatever within the brackets then for the multiplication or division then for addition or subtraction are this priority is clear are these priorities clear if you know the priorities you can solve the calculation and you can do the calculation in one step without having to write anything on the paper that is where you can save a lot of time otherwise if you write each and every step time is wasted okay guys are we clear so far shall we start with the chapter shall we start with the chapter everyone please do respond shall we start okay guys i'm not going to reveal the name of the chapter i would take you through a story a comic story which tells you the importance of the chapter all right shall we start so i would like to introduce uh two characters okay two persons two gentlemen okay mr cheska yeah and meet mr maskas so these two are very close to each other chaska is very naughty okay maska is more intelligent compared to jessica okay and he's a very foodie who cheska always likes to eat and always puts himself into trouble by doing something right which is not necessary so this is uh the introduction about these two characters all right cheska and muska right says kamaskar once it so happens that for some reason cheska is very sad and he's crying yeah he's crying don't you think so he's laughing is he laughing he's crying yeah feelings to some joke huh he's crying no yeah he's crying yeah okay fine so now being a friend of jessica muska has to help him right he has to ask right would you let your friend cry you would ask no so let's see what mascara ask hey jaska what happened why are you crying okay shaskar says i was in need of money when you are out of station so i took the money from don the local money vendor taking money the don warned me that if i don't pay me pay the interest and also the principal in time you will be killed but due to kovitt issues cheska could not run the business yeah properly so because of that he could not pay the interest and also the principal so now will the don leave him no he's chasing right so there's a reason why cheska is crying right now mascara what he says don't worry right what would be jessica's reaction you saved me right finally i got someone to help me right meanwhile maska doesn't i mean he doesn't allow chaska to celebrate he had something else to say hold on for a while i have something else to tell you let's see what he says you owe me money with interest he says interest of five percent per annum how much five percent per annum any guesses of chest cast reaction any cases again [Music] same thing right you also feel the same when your friend helps you out and he says you give me interest right there's no difference between don and uh the money vendor and his friend right okay but maska said you have completely misunderstood me has chaska really misunderstood maska not really right he felt those those naraha being a friend of mine he is asking for is helping me and he's asking for interest has he misunderstood no right you feel so right but according to maska chaska has really misunderstood maska in what way has misunderstood let us see what do you see here the price of coffee increasing it's just a commodity one of the commodity right it's a consumable right just a price of coffee in different various years what is happening increasing or decreasing increasing so increase in price of a commodity that effect is called as inflation right how much did muska ask five percent interest for his money why is he asking five percent interest for his money so is not asking for his profit he's just asking for reduction in the value of money guys say let's say muska gives jaska two lakh rupee today yeah gives jessica two lakh rupee today and say jaska is gonna return after two years after two years what with whatever uh muska could have bought with two lakh today let's say a piece of land you could you could you could could have bought right a piece of land with two lakh rupees not in cities okay power places you could have bought a piece of land but can he buy the same piece of land after two years with the same two lakh rupees definitely he cannot buy why because it will increase what is the defect called as inflation because of inflation effect the value of money will decrease so whatever the five percent musca is asking for it is not for his profit it is only to compensate for the reduction in the value of money the value of money will reduce with time it's not like two lakh is gonna become one lakh fifty thousand no two lakh will remain as two lakh but its value would reduce its value would reduce so whatever the interest that muska asked for it is only to compensate for the reduction in the value of money because of inflation effect so cheska has misunderstood musca right clearly he has misunderstood nascar now what would cheska feel now he feels sorry right for having misunderstood so obviously he'll feel he feels that it is fair enough five percent interest is fair enough because there will be an inflation rate of five percent per annum so i have to give him because he is helping me at the same time i also have to help him right so chaska feels it's fair enough right so you understood now the importance of money with time so what are we discussing time value of money so what are you understood by this money has a value with respect to time so today's 10 000 is not equal into 10 000 after one year agreed today's 10 000 is not equal into 10 000 after one year which 10 000 has more value today's ten thousand or one one year after uh-huh today's ten thousand will have more value ten thousand after one year will be lesser than two days because the value of money will decrease right see whatever you you could you didn't understand listen what is my question today is 10 000 okay and 10 000 after one year which has more value today still that's what you only said the answer today's 10 000 has got more value than 10 000 after one year or maybe after two years or maybe after three years right because of inflation effect the value of money decreases with time understood understood so what is time value of money money has a value with respect to time money has a value with respect to in fact the value of money will reduce with time right the value of money will reduce with time due to what due to what inflation you do inflation guys people thought that keeping money let's say you have a lumps of a huge amount let's say of 10 lakh okay so keeping money of 10 lakh for five years or maybe two years is it good keeping money with us only for five years or three years is it good it is not good first of all it is not safe first of all it is not safe the second thing is what the value of money will decrease with time right so people felt that keeping money with us for a longer duration is of no good so then they came up with an idea of investment so what is the investment suppose in the in the story which i narrated jessica wanted money mascara gave them money right system wanted money mascara gave them money right but did did muska gave the money just like that no he wanted an interest to it why interest to it because he wanted to compensate for the reduction in the value of money so so why the investment concept was introduced people who want money they can borrow it from people who have money with interest you understood the concept of interest why the interest has to be given for the investment the main purpose of investment was to compensate for the reduction the value of money later on it became for profit also later on it became for profit as well as compensation now for example let's say you have invested one lakh rupee in a bank fix a deposit so what is the fixed deposit rate in banks now six point five percent so let us make it ten percent the bank is doing very good let's let's say bank is bank has given you 10 per annum per month per annum okay that means how much interest that you get for one year 10 000 rupees so my question is is this 10 000 rupees what you get as interest is it completely a profit it is not a profit the main purpose of investment was to compensate for the reduction the value of money now is it's 10 000 only the comp compensation part no please understand whatever the interest that you get for your investment is called as nominal rate nominal rate so this nominal rate will have two parts in it nominal rate so whatever the rate of interest that is guaranteed for your investment is called as nominal rate this will have two parts in it one is inflation rate inflation rate the other one is real rate let's say in the market the inflation rate is six percent per annum okay so if the nominal rate is 10 percent how much would be the real rate for person because nominal rate is the sum of both inflation and real rates if the inflation rate in the market is six percent per annum then obviously the real rate is four percent now let us calculate how much is actually the compensation out of ten thousand and how much is actually the profit out of ten thousand see ten thousand is a surplus amount for your money right in addition to one lakh you get extra ten thousand rupees now we wanted to know how much is the profit part and how much is the compensation part okay guys ten percent is ten thousand now what is six percent of one lakh six thousand guys let me tell you clearly if you want to find out one percent of any whole number like this okay if you want to find one percent remove two zeros if you want to find 10 percent remove one zero from the right understood if you want to find one percent of any number remove two zeros or remove two numbers from the right so how many zeros are remaining one lakh has got five zeros if you remove two zeros three zeros are remaining one followed by three zeros is one thousand so what is one thousand one percent we wanted six percent so six thousand is inflation compensation inflation compensation and what is the profit so real real return is how much 4 000 rupees so for your investment there is a little profit there is a compensation part also so entire 10 000 interest whatever you get that is not the profit a part of it is a profit a part of it is compensation for the inflation effect so have you understood the concept of investment have you understood the concept of investment everyone online students please do respond have you all understood are we clear everyone clear so far everyone the first of this investment schemes was based on simple interest so we understood why investment is required and in investment how many i mean whatever the rate of interest is given for your investment it has got how many parts two parts what is that main rate of interest called as for your investment nominal rate and that nominal rate has how many parts two parts what are the two parts inflation rate the other one is real rate so it is a real rate that decides how much is a profit it is an inflation rate that decides how much is a compensation for the reduction in the value of money are these things clear now first of those investment schemes was simple interest okay let us try to understand what happens in simple interest guys in simple interest whatever the money that you invest so whatever the money that you invest is basically called as the principle that doesn't change you invest for five years or invest for 10 years or even it could be for 20 years also the principal whatever you invest that doesn't change it will remain the same okay so that is the characteristic of what simple interest the sum of money invested doesn't change it will always remain the same in case of simple interest so characteristic of a simple interest is what the principal or a sum of money invested will not change it will remain the same clear clear now let us see how a simple interest works okay guys i'm not giving to i'm not going to give you formulas straight away so we have not had started the actual syllabus yet so it's just the build up to the chapter so the main first concept of this chapter is simple interest rate away i could have given simple interest right on sis ptr by 100. so that's the first thing in your syllabus so this is a build up to make you understand the importance of simple interest the importance of compound interest importance of annuity all these things right okay so now let's see without the formula how a simple interest works all right please understand consider an example of rupees 50 000 invested for how many years three years at a rate of 12 percent per annum per annum means what for one year you get 12 percent on what on what whatever you invested 12 of your principle okay guys so let us see how it works out okay how many years investment three years so zero means the reference starting day how much is the principal fifty thousand now from zero to one how much time one year for one year what is the rate of interest twelve percent so fifty type fifty thousand into twelve press a percentage button six thousand so six thousand is the interest that you get for one year okay now at the end of first year will the principle change the sum of money invested doesn't change so principle for the second year will remain 50 000 only so from the end of first year till the end of second year what is the time duration one year so what is the interest for one year twelve percent on this principle how much again six thousand the principle at the end of second year will it change no it will remain as fifty thousand only and the interest for the third year again twelve percent on your money that is six thousand so total interest that you obtain is equal to six thousand plus six thousand plus six thousand plus six thousand and that makes it eighteen thousand okay let's say at the end of three years you get your amount invested along with that interest extra surplus amount so what is the amount that you receive at the end of three years amount received at the end of three years so what is it whatever you invest that is fifty 000 plus extra interest that is 18 000 so that makes it 68 000 so this is how a simple interest works is it clear is it clear this is how a simple interest works so have we used formula here we haven't used any formula theoretically we just saw how a simple interest works out is it clear is it clear so far now we are getting into the actual syllabus of time value of money right shall we everyone guys are these things clear so far please tell me that it is compensation given for the inflation please explain when does the principal amount change principal amount will not change in case of simple interest it changes in case of compound interest that i'll explain in case of compound interest you want me to explain this against shall we move on okay yeah now your actual syllabus starts formula for s i so you've learned sis ptr by 100 so that's only for your reference here after you will not be writing the formula p t r by 100 okay but still what is s i p t r by hundred what is p here principle whatever you invest is the principle and what is t time please understand time must be expressed per annum per annum that means uh in terms of years i'm sorry time should be expressed in terms of years okay because rate of interest is always expressed in terms of per annum for one year right so therefore the time should be expressed in years always for example if they say time is six years six years four months okay you have to convert this entirely into years only so how do you do this guys four months has to be converted into years how do you convert months into years four months first divided by 12 so this will give you the conversion of four months into years then it's not just four months along with that six years is that so plus six you need to do this will give you equivalent number of years how much it is six point so this is the time okay so for problems you should be first typing the time guys will it make any difference if i write 2 into 3 or 3 into 2 does it make any difference for multiplication order doesn't matter what i mean to say is if you have ptr by 100 you type p first or t first or r first does it make any difference no difference so whenever time is given in terms of years as well as months whenever time is given in terms of years as well as months please type time because you want to do the calculation in one step in the calculator okay so when you type time especially in time what is the first thing that you have to type months divided by 12 then what plus the number of years given to it so this will give you time in terms of years completely then what you do multiply that with principle and multiply that with rate of interest so this is what you should be doing you can get the answer in one step without having to write anything on paper if you type principle first then you then the conversion will not happen in one step if you do like that the calculation is going to be wrong have you understood everyone guys have you understood have you understood please tell me online students do respond guys any doubts please chat to the co-host please okay all right okay so explain again okay listen okay see what i said was time should be always t must be always in years time must be always in years suppose suppose t is equal to four years three months so this has to be converted into year so how do we do that first of all type the months first how many months three how do you convert months in two years divide it by 12. so this has to be carried out in one step in the calculator first type what months divided by 12 so this will take care of converting three months into equivalent number of years then what you do plus the number of years four so this will give you the equivalent number of years in the calculator in one step four point two five isn't it is it clear now is it clear yes now guys uh though the formula is ptr by 100 you will not be doing like this in the calculator in calculator in calculator what you do is in calculator s i is carried out this way p t r percentage because pressing divide then pressing typing 100 will take more time than pressing a percentage so especially when you need to find a simple interest what is the first thing you have to see see whether the time is given in terms of only years if it is given in terms of only years then whichever you type that doesn't matter principle you type first then time then rate of interest but when the time is given in terms of years as well as months the very first thing that you should be typing amongst ptr is the time only that to what you need to type months first then divide it by 12 then what the number of years four years right so plus four this will give you time in terms of years in toward the principle into what the rate of interest after that press a percentage button so by doing so you can get the answer in 10 seconds or maybe lesser than that you understood so time should always be expressed in terms of yes all right so what is r here s i rate per annum anna means per year all right now having seen the simple interest concept let us move on to amount okay so what we what did we do conventionally to get the amount whatever you invested plus the interest so can i write amount as a is equal to p plus s i p is the sum of money invested plus s i is the interest that you get for the given period of time you understood is it clear everyone is it clear online students guys respond are we clear so far okay shall we move on problems on s i yes i have classified the problems on si into various types the purpose of classifying the si problems on in various types is that it becomes easy for you to solve the questions quickly so you just have to identify the types if you can identify the types you can solve the question within 10 to 15 seconds any type for that matter so only thing that you need to spend on is identifying the types okay so i'll make you practice a lot so that even if i wake wake you up while you sleep okay and if i ask you a question on types definitely you should be able to identify okay so type identification becomes very very very important on simple interest guys simple interest it looks very easy sis ptr 100 a is equal to p plus s i but the varieties of question that they could they can form on simple interest is vast so type identification is very very important and you will not get these type identifications in any of the study materials okay icm ici will not give you these types they'll give you s is p t r by hundred a is equal to p plus s i straight away they'll solve problems on si and all conventional methods only right so type identification is very very important please do ask me if you get any doubt okay so first of all let's start with type one so what is type one yes to find si and the amount when p t r are given it's a straight question what will be given to you principle time and the rate of interest all the three will be given to you what will be asked simple interest and the amount it's a straightforward question type one is basically a stride straightforward question okay if you get this kind of question these are laddu questions so you should be blessed blessed enough to get such questions and questions have come on type one okay right so let us see the question you are you you understood type one how type one is will be okay type one will be what when p t r are given to find what s i and the amount okay let's take up the question guys p is given t is given r is given and what is that we are supposed to find s i and the amount guys s i is what p t r percentage tell me what is the first thing that you need to type in the calculator time in time what is the first thing you have to type first of all would you type 2 first no months 8 by twelve then plus two guys you're not supposed to write this on paper in the calculator itself first of all months divided by twelve plus what two then into what principle then into what rate of interest don't forget to press percentage after that what is the result so 899.99 that is 9000 isn't it have you all got the same answer everyone online students guys tell me is there any doubt with this guys along with the simple interest they have even asked what amount already simple interest is there in the calculator what do you do plus p you do you get the amount what is amount p plus s i answer is 34 000 you need not write anything on the paper already si is there in the calculator add what to it principle to it you get the amount guys have you understood should i explain again the calculations please do let me know yes are understood how about others 34 000 is the amount and what is si 9 000 right guys i want everyone to respond have you got the answer so if you do the calculation in one step like this how much time five to six seconds or maybe 10 seconds will it take more than that will it take more than that no right so type identification is very important it is type one ptr is given si you need to find and sometimes they may ask you to find amount if they ask you to find amount s i you know it will be there in the calculator by doing btr percentage plus what you do principle you get the amount guys clear everyone shall we move on to the next question yeah so tell me what is si for this and what is amount for this amount forty five thousand nine thirty seven point five is that the answer everyone got what did you feed first the time why given in terms of years as well as months in time what is the first thing that you would type months 3 divided by 12 plus 6 into 30 000 into 8.5 pressure percentage you get 15 09 37.5 add what to it to get the amount 30 000 guys unless uh it is asked don't do it if only si is asked you just stop at this right so in this question both side amount is asked so at principle principal to sr you get the amount that's it here everyone calculations clear guys online students clear once again fine yeah listen to me see to find s i what you need to do p t r percentage and what did i say time should be completely converted into years but look at the time here six years three months is that okay time should be always in terms of years months should be first of all converted so out of ptr what is the first thing you have to type whenever you get time like this time in the time what is the first thing you have to type that months how many months they have given three how do you convert three months in two years divided by 12 plus the number of years how much six so this will give you time in terms of years alone all right then into p press into button type p how much it is thirty thousand into our what is that eight point five press a percentage button after that you get fifteen thousand nine thirty seven uh 937.5 so that is s i and amount would be p plus s i just add principle to it it is 45937.5 so hope you understood now yes guy 3 is it clear okay so is type one clear so what is type one the ptr will be given and you'll be asked to find si or amount both will not be asked anyone right shall we move on shall we move on everyone typed two so let's see what is type 2 okay type 1 ptr everything will be given you'll be asked to find si and the amount type 2 is you'll be given amount time and rate of interest you'll be asked to find what is the unknown amount time and rate of interest will be given and you'll be asked to find what principle what is missing here principle is missing amount will be given to find p when amount time and rate of interest what's the difference between type 1 and type 2 in type 1 amount will be asked by giving principle in type 2 amount will be given they'll ask you to find principle you got the difference between type 1 and type 2 type 1 principle will be given type 2 amount will be given they'll ask you to find principle in type 2 questions okay this is what this is how you can identify type two guys why i say identify type types is because i'll be giving you shortcuts if you can identify the types you can apply that particular shortcut you can get the answer very easily okay now let us look into the question find the sum of money which amounts to 3720 in four years at six percent per annum guys listen to me carefully first what is this 3720 amount because they say find the sum of money sum of money always means the principle sum of money all invested always means what principle since they asked find the sum of money it means you need to find what principle amounts to 3720 means this is amount a and what is this for time t and what is this six percent rate of interest so a t r are given what is that we are asked to find principle find principle guys let us see how to solve this in a conventional method okay listen to me then you can copy it later you will get the notes also right don't worry about copying okay i'll give you enough time also to copy listen if you are looking to solve this question in a conventional method you have to use a formula which connects amount and principle this is as per si okay tell me which formula connects amount and the principle a is equal to p plus s i all right a is equal to p plus s i okay what is a given 3720 i would substitute p we don't know we will write as it is s i do we know no so we'll write ptr by 100 guys in the calculator if you want to do ptr percentage you can all right but on the paper ptr by 100 because we don't know one of the value there which value we don't know p we don't know right now what is common out of these p is common if i take that out it is 1 plus t r by 100 is equal to 3 7 2 0 then what you do substitute the value of t into r guys t is 4 and r is 6 divided by 100 plus 1 plus 1 1.24 p is equal to 3 7 2 0 then p is equal to what 3720 divided by 1.24 how much is the answer 3000 this is how you do solve this question conventionally okay you need to use the formula a is equal to b plus sr but this this is a slightly a lengthy procedure four five steps you have to write so let me now explain a method wherein without writing anything on paper how to get it yeah within 5 to 10 seconds you can get the answer but is it possible by doing so is it possible that you get the answer in 5 10 seconds definitely not so that's why i told you identify the types if you can identify the test because there will be a shortcut for each type you can just apply that and you can get the answer quickly so have you understood how we got 3000 as the principle in the conventional method should i explain again anyone wants me to explain this calculation online students please do let me know should i explain this again no anyone you understood sure okay shall we discuss the shortcut now yes what is that we need to find tell me principle what is type 2 amount time rate of interest are given what you need to find principle p is equal to a divided by 1 plus tr percentage that's all you need to do guys let me tell you first i already explained about the calculation tricks okay tell me amongst the numerator and denominator which is the complicated one here denominator in denominator which one would you type priority is given for multiplication or addition first multiplication so what do you type first t into r percentage what is t here 4 into r 6 press after that plus 1 what do you do with that store it now what do you do amount what is amount 3 7 2 0 divided by mrc then equal to what is the answer is it required to write anything on the paper no only thing is that the shortcut for type 2 you must know p is equal to a divided by 1 plus tr percentage have you understood what to type first is very important what do you type first denominator what is in denominator what is the first thing you need to type multiplication t into r what is t for rs into rs6 don't forget to press a percentage then plus 1 what do you do after that m plus y m plus to store it now numerator by denominator you have to do what is numerator 3 7 2 0 divided by what mrc ymrc denominator is in memory you need to recall it then press what equal to the answer is 3 000. guys have you all understood have you understood please tell me online students guys i'm waiting for your response so i said calculation plays a very very important role in maths and statistics yes anyone has a doubt please do let me know i shall explain again once again okay listen what is this type type 2 what is type 2 basically amount time rate of interest will be given to you what you'll be asked to find principle so short conventionally you're not going to do this method you're not going to do why it takes time now you're going to adopt a method which gives you the answer within no time so what is the shortcut p is equal to a divided by 1 plus dr percent for type 2 problem only thing is that what is type 2 you need to understand okay if you understand it is the problem is type 2 you can apply the shortcut and you can get the answer in one step what is the first thing that you would type is a numerator and denominator why complicated expression is denominator in denominator what is the first thing that you have to type multiplication that is t into r type t which is 4 into r that is 6 press what percentage then plus one what do you do with that store it by pressing what m plus now numerator is what three seven two zero what do you do with the numerator divide pressure divide by button then what do you do the value in the denominator already been kept in the calculator memory how do you recall mrc what do you do after that press equal to and the answer is 3000 is it here everyone please do respond is it clear type 2 yes shall we move on everyone so guys i'll be asking you randomly i'll just give after this class okay i'll be putting questions randomly and i'll ask you to identify which type so i'll not leave you just like that you have to identify the types see it's all about identifying the types because any type for that matter maximum 10 seconds sometimes maximum 30 seconds it cannot go beyond 30 seconds any problem for that matter okay look at this question a certain sum of money sum of money means what sum of money means what sum of money always means what principle a certain sum of money have they said about principle no some principle is gonna amount to how much 650 in six years at five percent per annum find the sum some means what are a principle some means principle isn't it type 2 the moment you come to know it is type 2 what is the shortcut p is equal to a divided by 1 plus tr percentage so what's the answer very good how many seconds you took five seconds to read the question it will take five to ten seconds to solve it 5 seconds or 10 seconds 20 seconds you will complete the question how many seconds you will have to solve the question 72 seconds still 50 seconds in your pocket right clear guys guys is it clear so far everyone have you all got the answer is 500 yes got it clear shall we move on to one more problem so what is fifteen thousand one twenty here what is fifteen thousand one twenty amount principle is how much you're insulting the problem by giving answer quickly how much is the answer please do it no problem what is t four years and what is the rate of interest six point five percentage and what's the shortcut a divided by one plus t r percentage twelve thousand is the answer yes very good guys one more one more i just put a question randomly let's see how much is the principle a certain sum of money becomes rupees eight thousand in six years as per si at 10 percent per annum find the sum amount is how much eight thousand how much is principle very good is it 5000 everyone so can you identify type 2 how do you identify type 2 amount time and rate of interest will be given and you will be asked to find the sum some means what principle clear everyone type 2 type 1 what is type 1 ptr given to find amount and s i yeah so is it clear so far type one type two everyone guys respond okay shall we move on to type 3 let's see what is type 3 s what is it to find r what is our rate of interest when a p t are given guys the main hint point to identify type 3 is you will be given principle as well as amount so there is one more possible question on type 3 tell me what is the similarity in a and b of type 3 both a and b amount and principle will be given what is the difference between a and b in a t is given r will be asked in b r will be given t will be us the concept is the same for both a and b of type three that's the main hint point of type three is what amount and principle both will be given in the question amount and principle both will be given in the question the moment you see principle and amount both in the question if both are there they'll give you time if they give you time they ask you to find what the only unknown is rate of interest okay both principle and amount they'll give you along with that they'll give you rate of interest only unknown will be time understood we'll take a question okay now you tell me by reading the question what is eight thousand and what is ten thousand eight thousand is principal and ten thousand is amount and what is given to us time is given to us what is asked rate of interest all right is it a or b it is a okay now let us solve this in a conventional method let's see how much time it will take guys you understood how to identify type 3 equation how principle and amount both will be present in the question the moment you see principle and amount it is type 3 is it clear guys is it clear okay now let's see the conventional method to solve this guys since both principle and amount are given in the question what is the formula in simple interest that connects principle and amount both a is equal to p plus s i isn't it a is equal to p plus s i now what do you do substitute for a what is a ten thousand substitute for p what is p eight thousand and what is s i p t r by hundred now what will happen this eight thousand would go to the left hand side become minus 8 000 correct so 10 000 minus 8 000 is equal to ptr by 100 correct now what do we know see this is going to be 2000 on the left hand side what do we know out of ptr by 100 we know p which is 8 000 what else do we know time that is 2 but we don't know what is r divided by 100 now what two zeros two zeros can be cancelled so hundred into twenty is two thousand and that is equal to eighty into two is one sixty where will that 160 go to the denominator is equal to r so r is how much percent eight percent guys tell me if you want to solve this like this how much time two minutes sir you're fast enough 1.5 minutes to 2 minutes now do you have any problem with the prop the same problem can be solved in 10 seconds do you have any problem if the problems can be solved in 10 seconds actually the problem is solved right your main problem is what time is the issue so if you can solve this in 10 seconds you have 50 seconds in your pocket extra yes have you understood this problem first of all conventionally how to solve this understood first of all can you identify this type how do you identify this type principle and amount both are given the moment you see principle and amount it is type 3 in type 1 only principle will be given amount will not be given type 2 only amount is given principle will not be given type 3 both amount and principle you can remember that way type 1 p will be given amount will not be given type 2 amount will be given p will not be given type 3 both amount and principle both will be given clear everyone guys clear shall we move on should i explain this conventional method again any online students who told eight percent two thousand by 160 how much [Music] i should not trust you guys twelve point five percent two thousand by 168 is you thought it is wrong your answer is wrong okay right i mean no online students identified that 12.5 is the answer right everyone understood the conventional method should i explain again not required sure and the most important thing what shortcut what is that we need to find rate of interest that's it a minus p divided by p divided by d into hundred do it what is a 10 000 minus p 8 000 would you multiply p t separately then divide no divide p first 8 000 then divided by t which is 2 into what 100 how much how much guys twelve point five percent guys a minus p what is a ten thousand minus what is p eight thousand do it in one step in the calculator ten thousand minus eight thousand divided by p first divided by what p which is eight thousand again divided by what t why because denominator always you have to divide into what 100 don't you get 12.5 okay guys type 3 only sometimes rate of interest is given means they'll ask you to find time okay same shortcut only only modification that you have to do is this r would go in the place of t and t would go in the place of r only t and r will get interchange that's it the formula the shortcut formula remains almost the same you understood for b so this is for a right this is for a rate of interest is asked suppose the time is asked what you need to do in the same formula interchange the positions of r and t that means t is equal to a minus p divided by p into r whole multiplied by 100 understood understood everyone is there any difficulty in identifying type 3 how do you identify type 3 principle and amount both will be there in the question sometimes along with principle and amount they'll give you what time they'll ask you to find rate of interest so anything by giving rate of interest if they ask you to find time anything the same shortcut formula what is it a minus b divided by principle divided by r if they ask you to find t a minus p divided by principle divided by t when they ask you to find r don't forget to multiply with 100 is it clear everyone have you got the answer as 12.5 by doing so everyone guys 12.5 is the answer shortcut love set conventional method now right see how much time you are taking how much time i am taking right shall we move on everyone guys online students no response i should ask all the time okay let's quickly solve these two questions also okay tell me is it type 3 how do you say it is type 3 question amount and principle both are given what is principle here fifteen thousand what is amount here eighteen thousand what is given along with that r what is asked time so if the time is of the rate of interest given divide r after dividing by p guys what do you do 18 000 minus 15 000 divided by what 15 000 then divide by what 5 into 100 what is the shortcut guys you need to find what your time a minus b divided by p into r into hundred what is the answer you got four yes understood type 3 understood principal amount both are given you need to find see rate of interest is given means time is asked look at this in what time means obviously time right t you need to find nice is it clear is it clear four years is the answer in next one what is asked rate of interest is asked that means r the same formula but we have to interchange r and t what is it a minus p divided by p into t whole multiplied by hundred answer is nine percent if the rate of interest is asked attached percentage if time is asked attach years that's it for uh you don't have to press it no no no no because this 100 will take care of that so unless see if i in the second shortcut i wrote p is equal to a divided by 1 plus tr person in the shortcut if i write percentage then only you press percentage and please don't press percentage wherever you want in the shortcut if it is there then only you press okay is there a is there a percentage here no so don't press a percentage for type three yeah everyone guys have you all got the answers have you all understood type three any doubts for anyone do let me know any doubts clear type 1 type 2 type 3 so explain once again bye right so these questions whatever we discuss so far are the questions on type 3 how do you say type 3 principle and amount both are given look at example two in what time rupees fifteen thousand amounts to eighteen thousand fifteen thousand amounting to eighteen thousand means fifteen thousand is a principle and eighteen thousand is the amount okay at five percent per annum they have given the rate of interest the see forget about the rate of interest the moment you see principle and amount both given in the question it is type three and along with principle and amount what they have given rate of interest so definitely you need to find time so the shortcut is t is equal to a minus b divided by p into r multiplied by 100 so what you do a minus p first that means 18 000 minus 15 000 then press the divide by button first divided by p what is p 15 000 then thinking that it's a multiplication don't multiply r is in denominator you need to divide press the divided by button then type r what is our five don't press a percentage is there a percentage in this no just five that's it in 200 so how much is that you get four understood tanya is it clear okay so in the next question you see at what rate of interest rupees six thousand amounts to rupees nine sorry six thousand amongst rupees nine thousand seven eighty so six thousand is principal and 9780 is the amount and along with that along with them they have given time so obviously the unknown is the rate of interest the same shortcut formula only rearrangement of the terms r and t so since we need to find uh r here send r in place of t and sign t in place of r that's it so a minus p 9 8 7 80 minus p is 6 000 divided by p that is 6 000 divided by t that is 7 and in 200 so it is 9 percentage understood clear so far everyone type identification also it's not just a shortcut and doing the calculation quickly i if you don't identify the types you can't apply which shortcut you have to do you will not know which shortcut you have to apply so identifying the question as which type of a question it is that is very important so why under each type i have given a note what is it for type one when p t r are given to find s i and the amount second type amount princip amount time and the rate of interest given to find the principle third p and a both are given in third there are two subtypes what is it if they give you uh time you'll ask you'll have to find r if they give you r you'll have to find t but the similarity in both this both principle and amount will be given in the question clear surfer everyone type three shall we move on shall we what is basically type forest two amounts in the bracket i have specified something what is it in terms of rupees sorry not rupees principle two amounts in terms of principle and time in the first case are given so that means first case are given means obviously there will be one more case so there will be two cases two amounts means obviously there will be two cases so you'll have to find time in the second case now first of all let me tell you what is the meaning of amount in terms of principle okay what is the meaning of amount in terms of principle guys say if i invest 10 000 and i get 20 000 as the maturity amount in return i'm going to get 20 000 after five years i invested how much 10 000 and i got 20 000 at the maturity what is maturity after your investment period whatever you receive that is maturity amount okay tell me what is ten thousand here and what is twenty thousand ten thousand is the principle and amount is twenty thousand so what do you observe here uh by looking at the values of principle and amount difference of ten thousand yeah one more thing what you can identify no no you said uh what is that you observe uh there's a difference of ten thousand rupees obviously principle is less than amount yes no no it's type 3 yes both principle and amount so what is that you can identify here i mean by looking at the values what you can make out amount is 20 000 in principle yeah very good amount is double the principle isn't it 10 000 is becoming 20 000 means it is into two right if i say 10 000 is becoming 30 000 it is into three amount is three times the principle yes so how to identify amount in terms of principle is they'll say certain sum of money certain sum of money doubles itself doubles itself what do you understand by this a is equal to two times the principle a certain sum of money doubles itself means amount is two times the principle can we not write a is equal to 2p for double and a certain sum of money certain sum of money becomes 5 times of itself a is equal to 5b so when you see such two amounts in the question in the question you should identify two two such amounts in the question double triple double five times five times seven times like this if you see two such amounts in the question it is type four understood you understood what is the amount in terms of principle double triple five times of itself eight times of itself this is what is the meaning of amount in terms of principle understood everyone if you see two such amounts in the question it is type four understood everyone is it clear the meaning of two amounts in terms of principle yeah okay now look at this question now and tell me how many such amounts such amount in the sense what amount in terms of principle a is equal to 2p how do you say a is equal to 2p money doubles that means a is equal to 2b there is one more such amount which is that 4 times so a is equal to 4p right so there are two amounts in terms of what principle the moment you see in the question two amounts in terms of principle it is type four first of all let me explain the conventional method okay don't you think that there are two cases in the problem one for the double one for the four times right guys is it understood there are two cases in the question one for double and one for four times guys if there are two cases there must be some similarities then only there will be a comparison right if there is no similarity you can't have a comparison i mean to say can you compare a commerce student with a science student you can't why the subject studied by the common students is different and that by a science student is different you can't have a comparison there should be some similarity yes you can come by compare students belonging to the same class because they study the same subjects they are taught by the same teachers you can compare because there is a similarity understood so for these two cases that is case one and case two there are similarities the first similarity for both the both of the both the cases is what what p same principle same principle what else will be same as the rate of interest both the cases rate of interest and the principle will be the same what else will be different amounts are different means obviously time taken will be different for these kind of problems please understand it's a comparative problem principle and the rate of interest will always be same for these kind of problems what will be different time durations are different if time durations are different obviously amounts are different don't you see two amounts are different 2p and 4p yes so what are we doing now we are doing the conventional method okay so case one is what a is equal to 2 times the principle case 2 is what a is equal to 4 times the principle okay now guys this is a equal to 2p means there is amount there is a principle in simple interest which formula connects amount and the principle a is equal to p plus s i let me use that a is equal to p plus s i now what do i substitute in place of a for the first case 2p so can i write a in place of a as 2p is equal to what b plus guys what is si ptr by 100 btr by 100 all right now this p would go that side becomes minus p so 2 p minus p is 1 p that is just a p right which is equal to p t r by 100 now this p and this p get cancelled yes how they get cancelled because this p when it is sent to the left hand side gets divided right p by b cancels okay so what are we left out with 1 on the left side that gets cross multiplied with 100 so 100 equal to tr tell me out of t and r what do we know for the first case time what is it six years and rate of interest we don't know that's what we need to calculate so what is our 100 by 6 keep it as it is 100 by 6 only keep it 100 by 6. now what next see whatever is the rate of interest in the first case the same is the rate of interest in the second case also and the principle is the same only the time duration will be different once again whatever i did for case 1 the same thing i have to do so what connects amount and the principle in simple interest a is equal to p plus s i what do i write in place of a for the second case for b and that is equal to b plus s i what is s i p t r by hundred guys if this p sent to the left hand side minus p so 4 p minus p is 3 b and what remains p t r by 100 what gets cancelled pp get gets cancelled 100 gets cross multiply or before that you can do something else here 3 is equal to t is how much we don't know we need to calculate r is how much 100 by 6 and in the denominator we have 100 we will have 100 so hundred hundred cancels so tell me what is t three six eighteen years long procedure right so how many years it will take for the same sum of money to become four times if it if it doubles in six years it will take 18 long years and the procedure is also long how much time it will take if you want to solve this in a conventional method two minutes but can you offer to spend two minutes to solve questions maximum 1.2 minutes not more than that 0.2 minute that is 12 seconds is required to read the question only understand the question only another 60 seconds you will have to solve the question if you spend so much of time in solving it like this you can't solve all the questions right so have you understood the conventional method first of all everyone guys you're not going to do this do like this for this for such questions you're going to do what apply shortcut so what we are going to do we'll see later but before going to the shortcut have you understood the concept first of all everyone is it clear if anyone wants me to explain again i shall do that clear so far clear okay shall we have the shortcut after the break i'll keep you waited for shortcut yeah so it's yeah we'll have a break for 15 minutes and after that we'll come back and have a shortcut guys all types will have shortcut time value of money because there's a value for your time there's a value for your money so more than money time has a value so that's what you're gonna learn so you're not gonna spend one minute to solve a question any question for that matter 99 95 percent of the questions can be solved within 10-15 seconds like this only without writing anything on the paper you know shortcut everything in the calculator right okay so after the break i'll be asking three types right the shortcut also [Music] so type 4 have you understood what is type 4 two amounts in terms of principle the moment you see two amounts in terms of principle it is type four conventional method we saw i mean we got the answer for this question as 18 years long procedure right so shall we have the shortcut for this what is that we need to find t1 or t2 time in the second case or time in the first case time in the second case so guys shortcut t2 equal to a2 minus 1 by a1 minus 1 into p1 okay what is a2 guys amount in the second case what is a1 amount in the first case let me take you through the previous slide guys tell me what is a 1 here double that means 2 times what is a 2 here 4 times that is 4. a 2 is 4 a 1 is 2 so what are you supposed to and what is steven six years and what is that we need to calculate t2 all right so what's the shortcut a2 minus 1 by a1 minus 1 into t 1 what is a 2 guys 4 times right 4 minus 1 3 type 3 in the calculator divided by a 1 minus 1 what is a 1 2 2 minus 1 is 1 only into t1 what is t1 t1 6 and the answer is how much time it takes if you do it this way 5 seconds what is that you need to do both from both the amounts you have to subtract one from both the amounts you have to subtract what one then divide the two amounts is it a one by a two or a two by a one a two by a two minus 1 divided by a1 minus 1 into what the given time duration that's it case 1 time you have to multiply this why we have to we have done minus 1 for both the amounts in the conventional method let me take you through the conventional method as you see if it is 2p on the left side this p will go on the other side minus p 1 gets subtracted here you see 4 p this p goes there and it will become 1 p gets subtracted 4 p minus p becomes 3p you understood so why minus 1 in the shortcut understood does it make sense understood so for type 4 problem what do you do a 2 minus 1 straight away in the calculator if amount is five times five minus one is four if the amount is four times second amount is four times four minus one is three type three straight away in the calculator divided by a one what is even in the question double that means 2 2 minus 1 is you need not do it 2 minus 1 is 1 any number divided by 1 is the number itself into what the time taken in the first case have you understood so what's the shortcut what's the shortcut a2 minus 1 by a1 minus 1 into what t1 do you have to write anything on the paper nothing on the paper everything in the calculator shall we have more questions so guys you need to identify the question type 4 tell me what makes you decide that this is type 4 question there are two amounts what are the two amounts four times and eight times so four times is a one eight times is a two what is t one fifteen years what is that we need to calculate t2 what is that you do eight minus 1 by don't do 4 minus 1 in the calculator 4 minus 1 is how much 3 straight away you type 3 into what 15 answer for t2 how much guys that is 35 no is it 35 guys i think you made a mistake 35 years yeah 35 35 yes understood understood any i mean how much time five seconds not more than that only thing is that you need to identify correct tell me next one is 30 what is even 3.5 times a2 is 8.5 times t1 is 10 so t2 is 8.5 minus 1 is 7.5 divided by 3.5 minus 1 is 2.5 into what 10. answer is answer is guys respond 30 years everyone got the answer solve one more okay i'll write the question pure practice a certain sum of money becomes six times of itself six times of itself in 12.5 years as per si as per si in how many years it would become nine times answer is what do you do second amount 9 minus 1 8 by first amount what 6 minus 1 5 into what 12.5 answer is 20 years five seconds understood only thing is that identify the type and apply the shortcut clear type four is clear everyone nice type four isn't clear now i'll write four questions you have to identify which type yeah can you try can you try so i'm not going to retain that in the slides okay you can write down the questions and you should tell me after me writing down those four questions you should tell me each question is which type and the shortcut right can you do that everyone each one of you should write down that okay because it will not be there in the pdf all right rupees 6000 amounts to rupees eight thousand or say nine thousand in five years as per s i find our which type type three how do you say type three both p and a are even so it is type 3 what's the answer what is shortcut for type 3 guys a minus p divided by p into t into 100 answers guys copy this down as as i said this will not be there in the slides all right this is for your practice and for you to identify which type it is right shall we have the next question what sum of money amounts to rupees 370 at eight percent per annum s i in six years first type of second type type 2 very good what makes you say that it is type 2 amount is given we need to find the principle tell me the answer what is p shortcut is a divided by 1 plus tr percent how much is the answer 2 very good 250 is the answer got it hope you're clearing the memory memory clear material okay next question a certain sum of money becomes becomes 1.5 times of itself in 7.5 years as per s i in how many years it would become 4.5 times of itself which type it is type 4 what makes you say type 4 two amounts in terms of principle so it is type 4 what is the answer t2 52 point is that the answer everyone check shortcut for type 4 52.5 a2 minus 1 divided by a1 minus 1 into what t1 guys is that 52.5 so every day i'll be asking questions i'll put the question randomly you should identify the type and should tell me the answer quickly right is it clear so far i'm not going to give a question on type one because it's a straightforward question right copied please all of you copy it because it will not be there in the slides okay explain third one yes okay a certain sum of money becomes one point times of itself that means 1.5 is the amount in terms of what principle and seven point sorry four point five times also is one of the amount in terms of what principle one point five times is amount in terms of principle and even four point five times is also one of the amount in terms of principle so two amounts in terms of principle they have given what's the shortcut for that t2 is equal to a2 minus 1 divided by a1 minus 1 into t1 right what is a2 here second amount four 4.5 five minus one is three point five straight away type what three point five in the calculator divided by press a divided by button what is a one minus one a one is one point five don't use calculator for doing one point five minus one answer will be wrong 1 5 1.5 minus 1 is how much 0.5 right straight away you should type 0.5 in the calculator into what p1 what is t1 7.5 years so don't you get 52.5 you understood clear everyone shall i clear this have you copied copying still copying finished online students shall i clear this done okay guys so we have done up to type 4 let's move on to type 5 let's listen okay type 5 so what is type 5 when two mounts in terms of rupees what is the difference between type 4 and type 5 there are two amounts in terms of principle here two amounts in terms of rupees what else and time durations they'll give you time duration for both the cases you'll be asked to find what principle and also si for this kind of problems the si rate per annum formula is si for one year divided by principle into hundred so this is the formula that you use to find sr8 per annum but remember for type 5 kind of a question you will be asked to find principle most of the questions asked so far is to find what principle so so rarely they ask per annum so even if they ask you to find sr8 per annum it's a just one step extended that's it okay so how to identify type 5 questions two amounts not in terms of principle in terms of rupees when you see two amounts in the question in terms of rupees it is type five okay two amounts in terms of principle type four all right okay now you should tell me what is 6900 guys please understand don't come to a conclusion that 6900 is the principal and 7500 is the amount what they're saying in the question a certain sum of money that means how much principle we don't know that is what you need to calculate so what is that they're giving 6900 is what amount in the first case a1 what is 7500 amount in the second case that is a2 all right all right okay there are two amounts in this problem in terms of what rupees so don't take 6900 as the principal and 7500 s amount what makes you decide against it because they say certain sum of money how much some they have not given that is what you need and look at the question part you need to find the sum and the principle i mean per annum right so some means what always so means what principle so principle is what you need to calculate if principle is what you need to calculate is it principle definitely not your understanding guys everyone are you understanding guys yes okay now let's see the conventional method to solve this question all right guys how many cases are there here how many cases two cases why how two cases two amounts there are two amounts obviously there are two cases so case one and case two all right what is case one amount a one which is six thousand nine hundred in how many years three years case two amount is a two which is seven thousand five hundred in how many years five years all right now since amount is given and we are asked to find principle what connects amount in the principle in simple interest a is equal to b plus s i tell me since the amount is for three years s i is also for three years simple interest is applicable for three years right so can i write s i as si for three years what is amount for the first case 6900 is equal to p plus si for three years let me call this as equation one okay do the same thing for the second case as well what is amount formula p plus s i for how many years in the second case for five years all right now have a look what is amount 7500 and p plus s i 4 how many is 5 years so call this as equation 2. so we have two equations with two unknowns what are the two unknowns one is principle the other one is s i rate per annum so two simultaneous equations you know how to solve two simultaneous equations tell me which one is easy to cancel is it principle or srsi for si principle you can easily cancel by doing what adding subtracting multiplying or dividing subtracting you'll do 2 minus 1 or 1 minus 2 2 minus 1 y 2 minus 1 amount in the second case is more than the first case so let us do what 2 minus 1 if you do so left hand side expression 7 500 minus 6 900 how much 600 600 and that is equal to pp cancels because you're subtracting and here s i for five years minus s i for three years the difference will be s i for two years two years right so if you look at they ask you to find sr8 per annum and you need si for one year correct si for two years is 600 what is si for one year divide by two si for one year is six hundred by two which is three hundred so we got s i for one year understood what do you do now substitute this s i for one year in any of the two equations let me substitute in equation one which one i'm substituting s i for one year so equation one is what 6900 is equal to principal plus si for how many years it is three years guys sri for one year is 300 for three years it will be 300 into three correct 300 into 3y into 3 because for 3 years into 3 you have to do for one year it is 300 for 3 years it will be into 3 right now this is what 900 where will this 900 go to the left side will become minus 900 so six thousand minus six thousand nine hundred minus nine hundred is six thousand and what is that principle is six thousand and is that the answer i mean final answer yes sum is six thousand but along with that you need to find something else what is it aside per annum look at the formula of acid per annum s i read per annum is equal to s i for one year what is s i for one year 300 divided by what principle how much 6 000 into what 100 how much 5 guys such a lengthy procedure how much time to four minutes right how much time it will take guys three to four minutes easily because so many number of steps yes and if you make a mistake in any of the steps will not get the answer right so can we solve this in 10 seconds or less than 10 seconds yeah we can with the shortcut what i am giving you it is possible right guys are you ready or have you understood this conventional method first of all see the procedure is simple right two equations you have you solve the two equations to find the unknown right simultaneous equation 2 minus 1 but here the problem is what actually time consumed you can't solve this in one minute that is not possible at all so we'll have to make it possible in 10 seconds how do we do it how do we make it possible that is by the shortcut so have you understood the conventional method first of all before moving on to shortcut everyone so what's the answer for this principle is 6000 and a second per annum is five percent shall we move on to shortcut guys yes shall we understood yes okay for this what is that we need to calculate principle and sr8 parana guys i'm going to give you principle one step shortcut one step shortcut to get the principle what did we do here what did we do here here we got the principle right almost at the last step last but one step we got the principle here we are going to get the principle in step let's see how yeah there are two amounts in terms of principle not principle in terms of rupees subtract the two a two minus a one divided by there are two time durations subtract the two t2 minus t1 all right all right there are two amounts in terms of rupees subtract the two in the numerator there are two time durations subtract the two in the denominator all right guys uh this will give you s i for one year s i for one year whatever i have written this within the brackets i mean this expression is basically what s i for one year okay now to get the see we are not finding s i for one here we are finding principle now right so multiply this with t one what is t one time in the first case so you may be thinking why t1 only if you want to do t2 you can do t2 also if you want to do t2 multiplied by time in the first case or time in the second case now what comes next depends upon what you have taken here all right what comes next depends upon what you have taken here since you have taken t1 here you have to subtract that corresponding amount t1 means first case time you have to subtract a1 from it and now suppose had you taken in place of t1 as t2 here you should have subtracted a2 in both the occasions you get the same answer guys and this value should be under modulus what do you mean by modulus if you get negative answer you have to make it positive so can you do it in one step now a2 minus a1 guys go back to the previous problem what is a2 7500 minus what is a1 6900 so what do you do 7500 divided by 6 900 what do you do after that pressure divided by button t2 minus t1 5 minus 3 which is don't do 5 minus 3 in the calculator please don't do that you will not get the answer 5 minus 3 in the in the mind itself divided by 2 you do into what t 1 in the first case what is the time duration 5 years or 3 years 3 years so into 3 you have to do then what minus plus or minus a1 what is the first case amount 6000 900 what is the answer you're getting what is the answer you get negative 6 000 but modulus of it you have to take the answer is 6 000 the only thing is that you need to practice this formula that's it what is it for type 5 a 2 minus a 1 in the numerator divided by t 2 minus t 1. that you need to remember and it depends upon the next thing if you multiply t 1 subtract a 1 if you multiply t 2 subtract a 2. do it with a t2 and a2 also you'll get the same answer do it again a2 minus a1 divided by t2 minus t1 after that what do you multiply t2 and what do you subtract a2 by doing this also you will get 6000 only check a2 is 7500 minus a1 is 6900 divided by t2 minus t1 is 2 into t2 is how much 5 minus a2 7500 you get a negative value but you have to take a modulus of it how much is the answer 6000 principle and guys i only i already told you this part let me mark it in different ink so that you'll identify whatever i'm identifying as a black one okay marking as a black okay this is what s i for one year not the everything whatever within the brackets in the black it is si for one year okay now guys s i rate per annum what is this s i for one year a 2 by a 1 by t 2 by t 1 what do you get 300 that is s i for one year divided by principle how much did we get 6 000 into 100 what's the rate of interest five percent per annum understood so this portion only will give you s i for one year t2 a2 a2 minus a1 divided by t2 minus t1 if you do you get s i for 1 a which is 3 300 divided by what is principle we got 6 000 into 100 you do you get the rate of interest understood everyone online students please tell me have you understood oh there is a litigation here have you understood everyone yeah i said it i'll explain again okay so what is this you got by doing this yeah sr8 per annum shortcut what is sr8 per annum si rate per annum is equal to si for one year divided by principal into hundred so which portion gives you sr for one year whatever in the black this portion is s i for one year if you want to calculate freshly you can do it what is a2 minus a1 7500 minus six thousand nine hundred divided by t two minus t one is two because five minus three is two so how much do you get three hundred divided by principle is how much already we got six thousand into hundred so how much it is five percent how much it is five percent understood understood so guys instead of multiplying t1 you can even multiply t2 also if you multiply t2 you have to subtract a2 understood understood can you do example two now first of all identify this as type five how do you identify this as type five answer is twenty thousand very good principle is ten twenty thousand yes absolutely correct what is sr8 per annum per annum is what s i for one year what is what is s i for one here this portion guys calculate a two minus a one divided by t two minus t one thousand six hundred divided by principle is twenty thousand into hundred how much percent eight percent guys you understood how do you how to get si for one year whatever i have encircled with the black color that is s i for one year and if you continue doing so you will get principle is it no no no no see oh it's the same okay i'll change the data i can always do it no shall i why do you worry i'm there yeah take the question a certain sum of money amounts to rupees rupees 6200 in two years and rupees 7400 in three years as per si find the sum and a sr per annum principle is 3 800 3800 sorry yes what is sr rate per annum what does it say for one year one thousand two hundred and the principle is three thousand eight hundred into what hundred and the answer is thirty one point five seven thirty one point five seven percent so type 5 comfortable only thing is that in different you have to remember the shortcut just remember what a2 minus a1 by t2 minus t1 into t1 if you do subtract a1 into t2 if you do subtract a 2 that's it and while you do t a 2 minus a 1 by t 2 minus t 1 write down that value somewhere y that is only s i for 1 here especially when do you write that whenever the question says find a sr8 piranha if they if they ask only principle then no need to write down that value see otherwise you'll have to find this 1200 again right a2 minus a1 by d2 minus t1 while calculating principle only whatever this within the bracket you write down that value somewhere 1200 you get right write down why because this for s rate per annum you need s i for one year which is 1200 for the last question which i gave you right divided by what principle which is 3 800 in 200 you get 31.57 percent very good guys is it clear so far everyone is it clear high five hope you are having fun with maths fun or boring boring 12 to 16 questions would come from this chapter guys come on chill 12 to 16 question and you're getting to solve that within no time should be happy no yeah should be dancing right shall we move on guys type 5 is it clear type 5 is it clear yes everyone how to identify type 5 two amounts in terms of rupees and two time durations given right shall we move on ah type six types after type six type seven type eight is i mean even if i don't give you type seven type it it's very easy actually up two types only eight see only eight you will get five questions guys from simple interest five questions you'll get from simple interest right sometimes see this type 5 whatever i just gave you sometimes on that particular type only two questions have asked two questions have come yeah so if you can identify the tribes and literally actually uh even though there are eight types to identify only five types only you have to identify understand first type it's a straight question ptr that's easy to identify type two type three type four type five this four types even type six five types you have to actually learn that's it type seven type type eight will be very easy even though easy i have included as a type seven and type eight okay so only these five types type two two type six you have to remember that's it okay guys listen what is type six when sr 8 per annum are different for different years sr 8 per annum are different for different years then to find s i so here also this is also not complicated why guys so far we used to have one rate of interest for the whole duration right so what is s i p t r by hundred suppose say the rate of interest are different for different duration for example say for first five years it is six percent for the next three years it is seven percent for the next two years it is eight percent so what do you see here rate of interest are different for different durations so that is how you can identify type six even if you don't identify it's the same formula ptr by 100 you should use but p1 t1 r1 by 100 plus p2 t2 r2 by 100 because there are different time duration different rate of interest the same formula only p3 t3 r3 by 100 and again in this type sometimes the principle can be same sometimes the principle can be different if the principles are same tell me guys what comes out p 1 p 2 p 3 are all equal they can be taken as p so p comes out p by 100 is out what remains within the brackets p 1 r 1 plus t 2 r 2 plus t 3 r 3 that's what i've written here when the principle is same when the principle is not the same it is this formula only but instead of writing divided by 100 divided by 100 divided by 100 for all its three terms you can write p1 t1 r1 plus p2 t2 r2 plus p3 d3 r3 whole divided by 100 you may be thinking why we are not pressing percentage you may be thinking p1 t1 r1 percentage plus p2 t2 r2 percentage plus p 2 t 3 p 3 t 3 r 3 percentage why not it is so why we are dividing by 100 guys if you press a percentage how many times you're pressing percentage for three durations three times you're pressing divided by 100 also you do i mean the calculation time is almost the same so i divided by 100 you do instead of pressing percentage all the time you can do it like this and you may be thinking why only three durations it can be two durations also it can be even four also so let me extend that's why i have extended here so on suppose if there are two durations the formula is restricted to only these two there are three different durations the formula can be written for three terms there are four durations for four terms and so on understood so type six actually literally type one only literally it's what type one ptr will be given right it's literally type one only okay so have you understood the concept so in type 6 principle can be same if the principle is a same p by 100 is taken out p 1 r 1 t 2 r 2 t 3 r 3 will be within the brackets suppose the principles are different for different durations obviously p1 t1 r1 plus p2 t2 r2 plus p3 dr3 and so on divided by 100 have you understood now if i give you a question you should be able to identify whether it is subtype 1 or subtype 2 principle being same or principle being different what is similarity between both subtypes what is the common thing between prince i mean subtype 1 and subtype 2 time and rate of interest are different that is similar right in both the cases time changes and even rate of interest are different yes okay you understood type 6 guys type 6 is literally what type 1 only but we are splitting si into we are splitting type 1 into 2 terms or maybe three terms or maybe four terms depending upon the given question that's understood so what you'll be finding out here total s i obtained that's type one also what do you find si only right here also we'll be finding si understood okay shall we solve the questions on type six okay guys have a look principle is same or different what makes you think this is type six seven percent for three years eight percent for two years and ten percent for next two years so rate of interest that's different for different years so what is that there was total s i accrued or obtained so what is total si what comes out what is common principle so p by hundred is out what remains how many durations are there three duration so t1 r1 plus t2 r2 plus t3 r3 guys you know this can be solved within the brackets can be solved in one step in the calculator using what multiplication m plus multiplication m plus multiplication m plus mrc please do it what is steven here three years what is r1 7 don't press a percentage here have i written a percentage here no that will be taken care of whole divided by 100 right so just type what 3 into 7 m plus next 2 into 8 m plus this is r 2 then t 3 is 2 years and r 3 is 10 2 into 10 m plus mrc into principle principle is how much 30 000 divided by 100 how much 17 100. is that the answer everyone got online students 17 hundred correct correct understood any doubt with this any doubt with this okay shall we move on everyone example two yes tell me principle same or different uh-huh look at the question carefully different how do you say different one-fifth of how much so first case principle is how much one-fifth of one lakh how much is one-fifth of one lakh it is twenty thousand what is p2 half of the money half of one lakh fifty thousand okay guys remaining from one lakh if you subtract the first two how much you get thirty thousand understood remaining means obviously how much guys from one lakh twenty thousand and fifty thousand if you subtract that means seventy thousand if you subtract remaining is how much thirty thousand so here principles are different even time durations are different and rate of interest are also different so what is total si yes p even t t1 r1 plus p2 t2 r2 plus p3 t3 r3 whole divided by 100 how much you can do m plus m rc right multiply the three terms first don't press a percentage why whole divided by 100 will take care of converting into percentage right 17 000 is that the answer guys you understood how come p 1 p 2 p 3 20 0 50 000 and 30 000 they've said one fifth of the money one fifth of how much one lakh that means one by five into one lakh which is 20 uh 20 000 next p2 is half of the money that means half of 1 lakh which is 50 000 remaining will be how much from 1 lakh if you subtract 20 050 000 remaining will be only 30 000. have you all got the answers guys i'm waiting online students how much you got 17 800 why you you took so much of time what made you take so much of time some mistakes in feeding the values oh you wanted to recheck how about others still doing it is any calculation uh difficulties please do ask me okay any difficulties in the calculation please do ask you're doing memory calculations only right m plus m plus m plus m rc finally are you getting 17 800 for this online students i did not get the answer from any one of you only one got 17 400 can we do the calculations diksha yeah see what do you do first p1 p1 is 20000 into t1 is 4 years into r1 is 5 press what m plus yes next p2 is 50 000 into t2 is 3 years into r2 is 6 press what m plus t3 30 000 into t3 2 into r3 press what m plus finally mrc then divide by what hundred don't you get yeah seventeen thousand eight hundred understood understood everyone clear shall we move on so let's see what is type 7 s to find t when an amount in terms of you guys we have seen similar kind amount in terms of p in which type type amount in terms of principle type 4 amount in terms of principle is type 4 here also amount in terms of principle only but what is the difference go back to type 4 and check what is the difference between that and this here also amount in terms of principle there also amount in terms of principle what is the difference there are two cases very good in which one type 4 but how many cases here an amount means what only one amount guys that is how you identify type 7 and type 4 type 4 similarity is what type 4 and type 7 amount will be given in terms of principle only but in type 4 two amounts in terms of principle but type 7 only one amount in terms of principle okay they'll give you one amount in terms of principle and they'll give you sr8 per annum they'll ask you to find time taken okay so what is the formula t is equal to that means time equal to total s i rate by s i rate per annum total sr8 by s i rate per annum okay guys in the uh description i have given amount in terms of principle but where comes total sr8 how to find out total sr8 when the amount is given in terms of principle see rate means what percentage right rate means what percentage so we want a percentage value for the numerator and we want a percentage value for denominator as well right essential always it will be a percentage but amount will it be a percentage no and we are not using amount for the numerator what else are we using for the numerator total s i rate say for example guys if they give you amount as certain sum of money doubles itself what is amount 2p okay please understand since we are looking for the rate that means percentage value for the numerator always amount should be first of all converted into percentage so tell me principal means what the sum of money that you invest see tell me rate of interest is always calculated on what whatever you invest let's say you invested one lakh what is ten percent of one lakh ten thousand what is hundred percent of one lakh one lakh only hundred percent of one lakh is the number itself right that the principle itself so please understand for type seven problem principle is always taken as hundred percent why are we converting amount into percentage because look at the formula we want total assign rate means what percentage only okay so principle is always taken as what 100 for type 7 problem so it will become what 200 percent guys still we haven't got total sr8 what we got is amount only so how to get totally silent listen guys what connects amount and the principle p plus s i what do i write in place of a 200 and what is p 100 we are converting everything in terms of percentage right p is 100 so what will be s i hundred suppose if amount is three 3p how much percent 300 if i substitute that 300 is equal to 100 plus s i what will be si what did you understand by this whatever is the amount total s i is always how much percent less how much percent less guys how much percent less hundred percent less if the amount is 200 percent total s i will be hundred percent that means hundred percent less if the amount is three hundred percent total s i is two hundred percent understood so you understood how to get the total s rate if you know the amount if they say a certain sum of money doubles that means it is 200 total si will be 100 that is what you will be typing in the calculator it is not 200 100 percent less you have to take and then divide sr 8 per annum let's say it is ten percent just divide by ten percent you get the answer for time understood so please understand for type seven problem always principle is taken as hundred percentage so whatever i have explained i'm going to show that now so for type 7 problems p is always taken as 100 percent why percentage tell me look at the formula we want everything in terms of percentage rate means what percentage only okay the total s i is always hundred percent less than what amount is that point justified why it is hundred percent less than how it is hundred percent less than amount always hundred gets subtracted from amount yes or no yes nice clear okay some examples if a is equal to 2p how much percent is a 200 percent so total sr8 will be 100 if a is equal to 4p amount is 400 so total sr it will be 300 so you need not write all this for your reference you have to write down but solving questions whatever is the amount subtract 100 from it and feed that in the calculator divide by the rate of interest given in the question you will get the answer in one step you need not write anything on the paper is it clear guys is it clear what to do in type 7 and what's the difference between type 7 and type 6 what is it what are the difference between type 7 and type 6 type sorry type 4 type 4 amount in terms of principle but two amounts type seven amount in terms of principle only one amount for type seven problem principle is taken as hundred percent why percentage because we want the rate numerator is also rate and denominator is also a rate so why we want percentages only so p is taken as hundred percent now tell me if i give you a certain sum of money becomes five times of itself so what will be total s rate 400 percent five times means 500 percent what is 500 amount is 500 percent total sr8 will be 100 less so 400 percent is what total s i rate have you understood sometimes sometimes they may give you time they may ask you to find sr8 per annum can we modify the formula so t will be equal to what sorry r will be equal to what total s i divided by time sometimes they'll give you time they may ask you to find a rate of interest again type seven how do you identify type seven tell me only one amount in terms of principle by giving rate of winter they may ask you to find time or by giving rate of i mean time they may ask you to find rate of it the same formula but only the modification you have to do rearrangement of terms have you understood everyone is it clear guys very often they ask questions on type seven very often right type seven type four even type three also i mean all types are very important so which time they ask we never know but if you know all types you can answer any question on simple interest so basically time value of money has three parts simple interest compound interest annuity take it from me simple interest compound interest if you want if you understand annuity is easier than these two concepts you can carry out the calculations in one step you can carry out the calculations in one step by just remembering one formula no types there annuity no types but in simple interest components there are some types okay you just have to practice that and remember the shortcuts if you remember the shortcuts you can do the calculations very fast so i'll make you practice more and more problems i'll keep asking you questions i will not leave you right okay shall we have questions on type seven yes okay example one a certain sum of money triples itself at five percent per annum s i find the time taken for the same what makes you say it is type 7 why not type 4 only one amount in terms of principle what is amount how much percent amount 300 total sis what you should be typing in the calculator 300 or 200 200 type 200 divided by what a sr8 per annum phi so what is t total s i rate divided by r 40 is the answer guys amount is given a is equal to 3 p right that means 300 percent total s i will be 200 don't write on the paper i mean now you can write for your reference but in the exam 100 less you take and feed that in the calculator r is how much 5 and the answer is 40 years understood understood so nothing bothers you in type 7 right what is the main thing you need to do you need to take total s rate always which is 100 less than amount that you type divided by if rate of interest is given divide that if time is given divide that you will get rate of interest in both the cases you need to divide only right if time is given divided by time you get rate of interest if rate of interest is given divide by rate of winter you get time in both locations you have to divide only understood everyone everyone yes or no here now you tell me the difference between example one and example two you tell me the difference between example one and example two what is given in as example one and what is given in example two i've given the s i in the second one first one amount is given here s i is given that means total s i is given off what is total s i total s i only is given 0.125 times of itself means principle how much is the principle to be taken as 100 so 100 into 0.125 12.5 guys do we have to subtract 100 now no why if the amount is given then you have to subtract 100 to get the total si what they have given is total si itself so what is that we need to find time taken what is time taken total s i rate divided by rate of interest per annum r which is 12.5 by 6.25 answer is two years have you understood the difference between the two questions have you understood the example yeah in the example one you see a certain sum of money triples that means it's the amount in terms of principle a is equal to 3p which is 300 percent and don't lesser it will be 100 less than that which is 200 percent but look at this question have they said certain sum of money becomes 0.125 times of itself no they've said s i on a certain sum is 0.125 that means it is a total si which is 0.125 into p p is how much you have to take it as 100 so 12.5 percent is total si rate and sr8 per annum given as 6.25 therefore total s rate is twelve point five divided by s r eight per annum is six point two five and the answer is two years have you all understood have you all understood clear explain again okay uh before me explaining please tell me have you understood example one i want to hear from you have you understood example one yes okay what is in example one certain sum of money triples that means amount is three times principle is that clear please respond for each and every point that i ask you yes okay so amount is 300 percent if the amount is 300 total si will be always 100 percent less that is 200 percent right 300 minus 100 is 200 divided by rate of interest given is 5 and therefore time is 40 years first problem is clear right now look at the second problem look at the statement of first problem okay they said a certain sum of money becomes three times but have they said certain sum of money becomes 0.125 times no they said what s i on a certain sum what they have given is total s i only they have given what is that equal to 0.125 times of itself itself means the sum principle so sum is taken as how much hundred percent so hundred into point one two five is twelve point five now we got total is sarah do we have to subtract this with hundred no when the amount is given then subtract the total s i only is given why do you subtract keep it as it is type 12.5 in the numerator divided by what is r given in the question 6.25 and the answer is two years is it clear now is it clear yes so i'll give you two practice problems now on type seven can you solve everyone yeah please solve this how to differentiate between this and type 4 please explain once more yes how to differentiate guys uh how to differentiate type 7 with type 4 in type 4 let me write type 4 one of the type 4 questions okay a certain sum of money sum of money becomes uh five times of itself five times of itself in say 20 years as per si in how many years in how many years it would become become eight times of itself look at example three and this question what i have written here in example three okay what i've written on the top tell me okay how many amounts are there in terms of principle only one amount a is equal to pi p but in in the example what i have written now right how many amounts are there a is equal to 5b and a is equal to 8b right there are two amounts in this question in terms of what in terms of what principle so that is how you identify type 4 question how do you identify type 7 question only one amount in terms of principle is that clear is that clear okay fine yeah guys tell me the answer for the first one answer for the first one is 25 years very good very good how did you get a is equal to 5p that means how much percent 500 percent what you should be feeding in the calculator 400 divided by rs 16 the answer is 25 years right and x 28. we'll check should be correct okay guys what is it they've said is it totally psi or amount total s i what is total s i given 9 by 16 into what 100 correct so which is 900 by 16 correct 900 by 6 keep it as it is okay now guys what is the formula t is equal to total s i divided by r okay cross multiply r into t is equal to total s i correct now what they've said in the question r is equal to t and what they've asked is psi rate per annum so in place of this t can i substitute as r only so r into r s r square r into r r plus r is r square which is total s i now guys tell me what is r root of total s i what is total s i 900 by 16 take your calculator 7.5 percentage what did you do uh you added r plus rs to our khmer guys 900 by 16 equal to then press the square root guys and one more thing for this kind of problems especially whenever they say the time is equal to s i rate per annum you can use i mean furthermore shortcut what is asked are right it is root of total s rate for what sort of questions if they say t is equal to r r is equal to d it will be just simply what root of total s i that's what we are doing right what is total s i 900 by 16 type 900 by 16 in the calculator press equal to press the root there's a shortcut for this shortcut again shortcut for what case tell me when t is equal to r and if they ask you to find the time or the rate of interest even if it is time same formula why because r is equal to t right r is equal to t so same formula is applicable let me write t is equal to r is equal to root of total s i have you understood guys have you understood have you all understood tell me clear anyone needs one more explanation on this no here we'll move on can 7.5 years and rate of what is it so can 7.5 as years and percent yeah 7.5 is number of years seven point five is the rate of interest because they have clearly said r is equal to t both can be same clear the last type of simple interest okay with this we are done so i would not consider this as one of the types but still i have given under eight type so basically there are five types that you have to remember what are the five types type two type three type four type five type seven type six is literally type one only so only five types the shortcuts you have to remember that's it okay so type 8 what is type 8 problems on 2sis there's no defined formula for this there will be 2 sis in the question you have to identify that's it there will be 2 essays in the question you just have to identify okay we'll have questions so that you will you'll only see the difference i mean what is given to us the s i on rupees one thousand at six percent per annum for a certain time duration is 30 rupees less than s i on the same sum at five percent per annum for the same time duration how many sis are there in this question two sis what is the first s i this is si1 which is second si this is si2 which si is more or which si is less si1 is 30 rupees less second one is more so second one is more than first one by how much 30 rupees so how do i write is it s i 1 minus s i 2 is 30 or s i 2 minus s i 1 is 30. s i 2 minus s i 1 is it see always greater value should be written first right which one is greater s i 2 is more than s i 1 by how much 30. so how do i write this s i 2 minus s i 1 is equal to 30 now you know what is si ptr percentage ptr by 100 tell me in both the sis what is same principle end principle and the time how do you say principle in the time the same rupees same same time duration same time duration and the same principle right same principle so since principle and the time are same can we not take them as outside divided by hundred what remains from s i to r two s i one is r one is equal to how much thirty now r2 minus r1 guys 6-5 how much 1 oh guys there is a mistake here this should be five this should be six correct first one should be five percent then only it will be less second one should be six percent please make the correction six minus five is one into p okay so what is the only unknown here t because p is thousand rupees we know so thousand by hundred is ten so you get ten t what is r two minus r one one is equal to 30 so 10 ones are ten threes are t is equal to how many years three years you understood you understood shall we again explain shall i explain again okay so there's a mistake in the question so this shouldn't should be a five percent or we can make a correction what is it 30 rupees less it's not less it's 30 rupees more we can make the correction like this correct if the rate of interest is more obviously the returns will be more right same principle same time duration obviously returns will be more in which case first case or second case which case rate of interest is more first case s rate of interest is more obviously first case s i will be more than second case so how many s i's are there here first case s i one and there are two s i's this is s i two so which si is more first so s i 1 minus s i 2 is equal to how much 30 all right now what is common in both the cases same principle so p outside what else is same time so p t by 100 is common what remains from s i one r one what remains from s i to r two and that is equal to thirty and guys what is p thousand p is thousand thousand by hundred is how much so ten t remains and what is r one minus r two one should i write that no ten t is equal to thirty that implies t is equal to how much three years understood is that clear is that clear everyone okay if that is clear tell me about the next question how many sis are there here in this question how many sis two sis which is more and which si is less huh which sr is more and which s i is less first s i is more than second s i so what do you write s i 1 minus s i 2 or s i 2 minus s i 1 s i 1 minus s i 2 what they have asked find the sum that means principle is equal to what what is the difference 450 rupees all right now what is common in both the cases principle is only the same right see s i on a certain sum at six percent per annum for four years is 450 rupees more than sr on the same sum that means principle is same anything else same no time duration and rate of interest are different so only p by 100 comes out what remains from si1 p1 r1 si2 t2 r2 is equal to how much 450. let's take your calculator do t1 r1 and t2 r2 in one step in the calculator how do you do that t 1 is 4 into r 1 is 6 would you press a percentage no m plus then t 2 into r 2 t 2 is how much 3 r 2 is 5 press what m minus y negative then mrc okay what is the value 9. so 9 p divided by 100 9 p divided by 100 is equal to what 450 so what we want actually p right correct so p is equal to 450 into 100 divided by 9 correct what is the answer huh 500 is it 5 000 5 000 guys is it clear is it clear is it clear everyone simple type 8 right there will be two ss could be sometimes difference could be sometimes addition also s i 1 minus s i 2 or s i 2 minus s 7 depending upon the question and the common things has to be taken outside whichever is common in both the cases from the in the first problem p and t both are common we took it outside second problem only principle is same we took only b by 100 outside that's it have you understood type 8 everyone clear or not here everyone one more time second one first one second one fine uh how many sis are there in this question two sis which is more first one or second one first one is more than second one here is there any difference with that i mean uh the dot with that s i one is more than s i two so since s i one is more than s i two we can write s i one minus s i 2 is equal to how much what is the difference 450 rupees look at both the cases what is same same sum that means principle is same what else is same nothing else is same because here time rate of interest time rate of interest are different so if that is the case from the first one t1 r1 will remain the second one t2 r2 will remain and that is 450 t1 r1 and t2 r2 can be solved in one step in the calculator what is t1 for into r1 is 6 would you press a percentage now no divided by 100 will take care of it okay t i mean 4 into 6 m plus then 3 into 5 m minus y minus negative sign then mrc how much do you get 9 right so 9 p is equal to 450 followed by how many zeros two zeros if you cross multiply hundred so therefore p is equal to forty five thousand by nine is how much five thousand have you understood now here have you understood so how many types in si eight types there are eight types in si so literally you need to remember how many times five types type 2 type 3 type 4 type 5 type 2 type 3 type 4 type 5 that means 4 along with that type 7. if you remember this your essa is complete okay uh i i will let you solve icn material equations because before solving icm mutual equations you must know all types so let's consolidate whatever we have learned so far right type one tell me how do you identify type one p d r are given to find to find s i and amount type 2 to find principle when a t r are given to find principles type 3 how do you identify no no what to find you forget about that what will be given a and p will be given then it is type 3 along with a and p if they give you rate it will be time you need to find out what is it t is equal to a minus p divided by p into r whole multiplied by 100 all right if they give you time instead of r r is equal to a minus p divided by p into r p to t sorry p into t into 100 this is type 3 how do you identify type four two amounts in terms of p what is the shortcut for type four a two minus one by a one minus one into p1 by four type five two amounts in terms of rupees and time durations okay so how do you do it by shortcut method a2 minus a1 by t2 minus t1 multiply if i multiply t2 minus a2 and the modulus of this you have to be t have to be taken okay this is type 5 what is type 6 si rates are different for different for different duration okay what is type 7 only one amount one amount in terms of principle okay uh what is principle to be taken as for type seven hundred total s rate will be always hundred percent less or more less than amount what do you divide that by is or time if they give you time divide by time to get the rate of interest if they give you rate of interest divided by i clear is it clear okay that is type 7 and you know type 8 what is type 8 problem song guys this whatever i have written you have to consolidate si this way write down all the types in one page that should give you all shortcuts all eight types so you can't refer back all the time right you can't refer back all the time so you today end of the day after reaching home make a short note of simple interest having all eight types written on one page each type type identification shortcut type identification shortcut because whenever you feel like you can refer to it and you can remember it yeah if you do this your si is done do this first then solve ica material questions you have any doubt you ask me okay so what you learned now is massive what is there in icis it's a tank what you learned is ocean you will understand by by looking at the questions of icy and material okay so please do that today complete everything so tomorrow we should start with component is before i start with compound interest i would put some questions you should be able to identify the types yeah all of you should come prepared online students can you come prepared i'll put some random question you should identify the type and also the shortcut yes can you do that can you do that you do that if you do this keep doing this for the rest of the chapters for even when for all mathematics you know logical reasoning how easy it is math is much easier than that only thing is that awareness so few people will have that what in their mind max is difficult for me actually not if maths is made easy it will be easy hope i am making it easy yeah okay right so please come prepared all right let's have the discussion tomorrow all right thank you good night [Music] very good evening everyone right so are you all ready with all the types can you identify the types yeah i'll just ask you questions now which type you should tell me i'll just give you data you identify which type yeah okay are you ready guys are you ready online students and it's not just the type identification the shortcut also you must tell right okay right should i give you data okay the data is a certain sum of money certain sum of money becomes rupees 6500 in three years and rupees 7250 in four and a half years as per si find the sum which type which type how type 3 two amounts means two amounts in terms of what is it in terms of principle come on two amounts in terms of rupees which type type five ah what's the shortcut a2 minus a1 divided by t2 minus t1 into if you multiply t2 then instead of multiplying t2 if you multiply t2 then what you have to subtract minus a2 if you multiply t1 minus a1 so what does i rate per annum formula for type five problems no what is a2 minus a1 divided by that is si for one year s i for one year divided by what principle into hundred that is type five identify two amounts in terms of rupees is type five yes yes everyone what's the answer for this my question is only to find the principle what is the principle do it guys what's the answer for principle 5000 very good four and a half means what four point five no four point five minus three that is one point five so what is a two minus even six seven thousand two fifty minus 6500 divided by 1.5 into what 5000 is the answer p is equal to 5000 yeah type identification is very important yes can i ask you more questions identify the types yes tell me what if i give you in what time in what time rupees 8 000 amounts to 12 000 at 10 per annum s i which type type 3 what do you how do you say it's type 3 time ok fine how do you identify this is type 3 question amount and principle are given amount and principle are given the moment you see amount and principle both be being given in the question it is type three what is that what is that we need to calculate very good five years yes what is that we need to find t so what is the shortcut a minus b divided by p into r all multiplied by what hundred what is a here in this question twelve thousand what is p 8 000 answer five years five years yeah one more guys understood a certain sum of money becomes three times of itself three times of itself in 8 years as per si in how many years in how many years it would become six times which type very good type four how do you say type four how do you how do you know it's how do you say it's type four how many amounts are there three times is one amount six times is another amount amount in terms of what principle correct three times how do you write a is equal to three p six times means a is equal to six feet two amounts in terms of principle which type type type four what's the shortcut for type four a2 minus 1 divided by a1 minus 1 into what d1 what is a1 a2 minus 1 6 minus 1 is 5 type 5 in the calculator divided by a1 minus 1 to right into what t1 what is t1 here 8 answer is it 20 20 or 15 20 years check once 20 sonya you have to check with your answers it's not 15 it is 20. yeah understood type 4 why how type 4 it is two amounts in terms of principle two amount in terms of rupees type five principle amount both given in the question type three amount given to ask i mean to find principle amount time rate of the interest are given and to find the principle type two okay shall we have an expression okay so it's only to identify the types so i am giving the questions okay a certain sum of money a certain sum of money becomes four times of itself four times of itself in 12 years as per si in how what is the rate of interest find the s i rate per annum type which type very good i got the answer already only right how do you say type 7 how do you say type 7 how to identify type 7 only one amount in terms of principal do you have any other amount except four times here only one amount if you have only one amount in the question it is type 7 so type 7 answer is 33.3 okay we'll check so what is type 7 total si divided by sr8 per annum is asked actually time is given so they get into change what is total s for type seven problem p is taken as how much percent hundred so amount is four hundred percent means what is total si three hundred so you type what three hundred in the calculator divided by time is how much twelve how much is 25 check with the answer again it's not 33.3 it's 25. 25 years yes are you getting it you're not revised few types you're able to identify other types you have to remember the types type identification is a very important thing here so how to identify i told you if you see only one amount in terms of principle it is type seven if you see principle and amount both given in the question it is type three if you see two amounts in terms of rupees it is type five if you see two amounts in terms of principle type four that is it if you remember five types which type i said type two type three type four type five and type seven other types even if you forget also you can do the question and questions easily but these types are required to be remembered because there are shortcuts here yes so have you understood have you understood so shall we solve the exercise questions on si quickly will solve it then we will move on to compound interest okay so we have done so much now let's see how will you identify the questions look at the first question guys s i on rupees 3500 for three years at twelve percent per annum what are given principle time and rate of interest so what is that we need to calculate s i correct type one so what is s i p t r percentage here time is given in terms of only years you can multiply whatever you wish first 3500 into three into 12 percentage answer one two six zero so this is type one easy question right you understood how about the second question type one only ptr percentage here also rt is 4.5 you can straight away feed what is si what how much it three seven eight three three seven five okay option a three three seven five now tell me they have given i they have given principle and they have asked us to find what rate of interest they've given time also they've given i i means what interest s i so what is s i first of all p t r percentage correct ptr percentage or ptr by 100 because we don't know r right we don't know do we know how r we don't know right so obviously what si is how much 300 so 300 in 200 is 30 000 ah now where will this pnt go to the denominator right to the denominator and what else t is how much one so how much it is six percent you can do this in one more method guys how you can do this in one more method huh type two you can apply how see for type two you must know amount right what is amount basically p plus s i we know p which is five thousand we know s i which is 300 so 5 300 is the amount amount time and the rate of interest or rate of interest is not known amount we know you know the principle amount principle you know can't you find out r how a minus b divided by p t into 100 you can do like this yeah what is a minus b 300 divided by what is p 5 000 divided by what is t 1 into 100 how much is the answer 6 if you see a minus b basically what s i only right what is a minus b so you can straight away substitute a minus b is s i they have given of s i is it required to do a minus b see a is equal to p plus s i okay so s i itself is a minus b correct so in place of a minus b we can substitute s i only right you understood so it is type three clear so if you use this what si formula p t r by hundred you'll have to write the steps it'll take more time yeah you can do that literally it's the same no a minus p is s i divided by p t into 100 it's the same actually right so since you know type 2 you can apply type 2 here that's it type 3 sorry yeah have you understood everyone guys online students is that clear is that clear yes okay shall we move on to the next question okay tell me about this p is given a uh a is given so what is s i a minus p i a is equal to p plus s i now so s i will be a minus p subtract the two you get s i how much it is two thousand seven hundred a is seven thousand two hundred p is four thousand five hundred subtract the two you get the answer two thousand seven hundred clear next question p is given a is given t is given we need to find r which type type 3 the moment you see principle and amount it is type 3 you may you may be asked to find r or you may be asked to find t what is asked here in this question r so what is our a minus b divided by p into t into hundred one step what is a minus p sixteen thousand five hundred minus twelve thousand you need not do that right four thousand five hundred straight away you can type in the calculator divided by what divided by what twelve thousand divided by t means two point five into hundred how much fifteen percent this is which type type three understood now next question s i is given it's i means actually s i okay s i is given p is given r is given in the time again type 3 you can use a minus p is si only right you can use type 3 which is what is that we need to calculate t so a minus b divided by p into r into 100 so s i itself is a minus b current you can straight away substitute 2 500 in place of a minus b divided by p is 10 000 divided by r is 12.5 into 100. how much is the answer two years see that is the importance of knowing the types if you know the types you can easily solve the questions is it clear guys everyone is it clear online students guys waiting for your response yes shall we move on ah we are done with all the questions right have you left out any question oh three questions are left out how come p is equal to eight thousand five hundred e is equal to ten thousand ten thousand two hundred okay twelve and a half percent t will be which type type three so what is type 3 a minus b divided by p into r whole multiplied by 100 so what is that we need to calculate time what is the answer how much 1.6 years options can you tell me the options for this one year seven months okay option b two years 1.5 years what will be your answer first one is the right answer guys please understand 1.6 years is what you got the answer is right 1.5 years means 1 year 6 month so 1.6 years means approximately one year seven months if you want you can see seven divided by twelve you see seven months divided by twelve what is the conversion approximately zero point six approximately 0.6 so 1.6 yes means close to one year seven months so it's not 1.5 years 1.6 means what 1.6 years means it is not one year six months it is one year seven months approximately is it clear is it clear everyone online students nice shall we have the next question the sum required to earn monthly interest of 1200 18 per annum si so what is it they have given si they have given off they are asking us to find p that option is c no that is not one point five years that's what i am saying now one point five years means one year six month six months will be equal to 0.5 years half a year means what six months correct half year means six months so seven point six years means how many months point six into twelve you do now it's point yeah 0.6 into 12 you do approximately 7 months you understood see 1.5 years means one and a half year means what one year six months yes but 0.5 years means how many months six months but what is that we got is it one year six months or one point six years whatever answer we got it is not one year six months it is 1.6 years right your calculator is showing the value as 1.6 that means it is a year's time in terms of years alone so 1.6 years means one year seven months approximately understood so if you want to confirm point six into twelve you do point six years into years means seven point two months point six years into months if you to do 0.6 into 12 you do 7.2 months approximately 7 months it is understood yeah guys is it clear the sum required to earn a monthly interest of thousand two hundred and eighteen percent per annum guys look at the rate of interest per annum it is what they said monthly interest of 1200 since the rate of interest is given per annum monthly interest also should be this interest also should be for per year so per year interest is how much 14 000 what is that they're asking us to find principal so guys s i s i for one year we got 14 400 s i rate per annum is also we know 18 how do you find the principle guys you know s i rate per annum is equal to s i for one year divided by p into hundred ti-fi concept see what is the only unknown here sr at per annum we know si for one year we know the unknown is p so just cross multiply s i for one year is 14 400 sr rate per annum is 18 into 100 how much it is 80 000 understood see please calculate the s i for one year because s i for one month is thousand two hundred per year means into twelve you have to do so you get how much fourteen thousand four hundred so what is this s i for one year interest for one year if you know si for one year and sr rate per annum can't you find out the principle prince sr-8 per annum is s i for one year divided by principle into hundred so only unknown is p cross multiply p there and s rate per annum will go to the denominator so 14 400 divided by what 18 into 100 so that is the principle understood is it clear everyone online students please do respond is it clear explain again see what is the question what sum of money what sum of money will will be invested will be invested to earn to earn a monthly interest of interest of rupees one thousand two hundred at eighteen percent per annum s i okay so s i rate per annum they have given and monthly interest is one thousand two hundred yearly interest that means s i for one year will be 12 1200 into 12 right per month it is 1200 into 12 if you do it is 14 400. what is this s i for one year s i rate per annum is how much percent 18 percent so what is the relation that connects si for one year s i rate per annum and the principal s i rate per annum is equal to s i for one year divided by principal into hundred isn't it sr8 per annum is s i for one year divided by principle in 200 so where will this p go to the left side s i for one year s i for one year divided by s i rate per annum into hundred so take a calculator now s i for one here is fourteen thousand four hundred divided by s r eight per annum is how much eighteen into hundred if you do you get eighty thousand or else you can do one more thing si for one year you write down fourteen thousand four hundred okay fourteen thousand four hundred can you tell me the options for this question fifty thousand sixty thousand uh eighty thousand no no no that's none of this this you can do by option heating also first of all you must write down what is that s i for one year how much it is fourteen thousand four hundred now so always when you are plugging in the options when you are hitting the options i mean when you're doing option hitting method always choose a moderate option which is a moderate value here 60 000. so how do you say it's a moderate option because you have a value less than sixty thousand and you have a value more than sixty thousand also so sixty thousand is a moderate value now choose sixty thousand as a principle and find out the s i how do you find s i p t r percent p is sixty thousand into t is one year r is how much 18 how much do you get do it 60 000 into 1 into r is 18 pressure percentage how much it is 10 800 so it is lesser than 14 400 guys for 60 000 only you're getting lesser for 50 000 still it'll be lesser so obvious answer is 80 000 if you want to can check 80 000 into 1 into r 18 press a percentage don't you get 14 400 you can do it that way also but you must know what is a psi for one year not si for one month why it's not si for one month because rate of interest is given per per annum so si is also should be converted for one year is it clear you can do it that way also everyone understood guys clear how many more questions two more questions okay we'll finish it off then we'll start with compound interest yeah tell me the next question quickly they've given us a two only no no you tell me the question however it is given a sum of money amounts to amounts to six thousand six thousand two hundred in two years seven thousand four hundred in three years as per six guys we have solved this question which type it is first of all which type guys type 5 so what is type 5 how do you find principle a2 minus a1 divided by t2 minus t1 into if you want to multiply t1 you can multiply then subtract what a1 quickly guys after this whatever within the bracket you write down that value how much is sr for one year a two minus a one divided by t two minus t one thousand two hundred uh so that is what s i for one here continue doing multiplication with t one into two you do minus a 1 how much so principle is 3 800. have they asked the question to find only principle no they've asked us to find the essential so why i wrote what is i for one year off immediately after this right this itself whatever i am marking here that itself is what s i for one year now what is sr8 per annum si for one year which is thousand two hundred divided by principle which is three thousand eight hundred into what hundred how much person thirty one point five seven percent the same question i think i have solved right is that clear everyone is that clear think of doing this problem in a conventional method we'll all become old guys understood yeah yeah last question a sum of money doubles itself doubles itself in 10 years the number of years it would triple itself as option a 20 25 50 yes 15 years and no no no okay guys which type of a question is this which type type 4 how do you say type 4 amount in terms of principle how many amounts what are the two amounts double as one amount and triple is another amount two amounts in terms of principle it is type four what is the shortcut a two minus one divided by a one minus one into what t one a 2 minus 1 is 3 minus 1 is 2 divided by 2 minus 1 is 1 2 into what what is steven given 10 answer is so what is this t2 20 years duster understood clear so that's what remember all the eight types shortcut you apply you can get the answers quickly yeah i'll keep asking the types that's that's the only thing in time value of money if you identify the types you can easily do it otherwise you'll waste a lot of time in solving the question so please list all the eight types in one page one paper one sheet of paper then you can always have a glance at it right hope you all have done that online students have you done that yesterday i told you to do so right have you made a short note of it tell me how many of you made only one s how about others yes so shall we start with compound interest guys please focus what remember things all right identifying the types is important identifying types also it's very easy what tell me if there is only one amount in terms of principle which type type seven two amounts in terms of rupees which type type five two amounts in terms of principle which type type for principle and amount both are given which type type 3 amount given time given rate of interest given to find principle which type that's it that's it so you're done with the simple interest only thing is that you need to practice the shortcuts that's it okay so shall we move on to compound interest this tell me what is the characteristic of simple interest i told you a point about simple interest the characteristic principle remains constant it doesn't change for any amount of time that you invest your money for right so if you invest for five years the principle remains let's say one lakh you invest it'll remain as one lakh only for the calculation right it will it will not change compound interest guys why the concept of investment was introduced people thought that keeping money with us only for longer duration of time is not good why the value of money decreases with time due to what inflation so people they wanted compensation for the reduction in the value of money so they came up with an idea of investment but whatever the interest that you get for your investment is called as what whatever the interest that you get for your investment is called as what very good nominal rate that nominal rate has got two parts inflation rate and real rate so which part says how much is a profit for you real rate which part says how much is the compensation for the money inflation rate so you understood that your investment is not only for the compensation of for the reduction in the value of money it is also for little profit as well right so people thought that with simple interest whatever the returns used to come was less so they came up with a new idea called compound interest where the returns can be more how it can be more is here the fact that the principle is going to change at every compounding what is basically compounding it's a stage where the principle changes it is a stage where the principle changes if the principle changes once in a year it is said to be annual compounding or yearly compounding suppose if the principle changes twice in a year it is said to be half yearly or semi-annual compounding if the principle changes four times in a year it is said to be a quarterly compounding if it happens 12 times in a year it is monthly compounding so these many types of compoundings you've got in compound interest so what is basically compounding the principle changes right once i mean once in a year or once in a half year or once in a quarter or once in a month depending upon the type of compounding that is what is called as the change of principle is only called as what compounding what is compounding the change of principle is only called as what compounding please make a note what is compounding means change of principle so p changes at every compounding this compounding can happen once in a year as i said once in a half year as i said could be once in a quarter or once in a month now the same way as we did for simple interest if you remember right before the formula approach i explained the theoretical approach how a simple interest works right hope you remember that do you remember that everyone guys you remember that right so how did we do we drew a line dividing the line into number of parts equal equal to how many years i mean equal to number of years so there it was three years only here also it is how many years three years what's the principle here fifty thousand invested for three years at twelve percent per annum if you remember it's the same example but it was on simple interest basis but this is on compound interest basis what do you understand by compounded annually the principle is going to change once in a year so let's see how it works okay to start up with what is the principle guys 50 000 to start off with the principle is 50 000. now for the first year what is the interest that you get 12 percent per annum right 12 on what the principle 50 000 into 12 press a percentage how much it is six thousand guys is it clear so far online students is it clear so far okay now what happens at the end of first year see in case of simple interest the principle do not change right it will not change it doesn't change right but in case of compound interest principle changes so what will be the new principle the old one which is 50 000 plus the interest that you obtained for the first year which is 6 000 so that makes it 56 000 as a new principle clear now what is the interest for the second year it is 12 only but on what the new principle so what do you do type 56 000 into twelve pressure percentage what is the interest six thousand seven twenty so that's the new interest for the second year that's the interest for the second year now tell me at the end of second year what is the principle fifty six 000 plus what the interest that you obtained for the second year which is 6720 tell me how much is the new principle 62 720 now tell me the interest for the third year the new principle is 62 720 and the rate of interest is 12 per annum how much it is 526.4 now the total interest that you get for three years is how much add all the interest six thousand plus six thousand seven twenty plus seven thousand two five twenty six point four six point four how much seventy thousand no no i'm just asking you the total interest total interest that's it how much 20 000 to 46.4 guys if you remember in case of simple interest how much did we get this for the same example eighteen thousand every year six thousand six thousand six thousand so it was eighteen thousand for the same example but it was on a simple interest basis but compound interest basis how much you're getting twenty thousand two forty six point four isn't it more than simple interest you're getting more interest in case of compound interest than the simple interest what is the reason for that because principle is changing every year in case of simple interest principle doesn't change it'll remain the same so why the interest for every year will be the same in case of si so here the principle changes what i mean at every compounding could be every year could be every half year could be every quarter or could be every month understanding right so but in case of simple interest the principle doesn't change so the interest that you get in case of simple interest is lesser compared to the interest that you get in case of compound interest have you understood guys have you understood the theory of compound interest how it works now tell me what is the amount that you would receive at the end of three years what is the amount whatever you invested that is 50 000 along with that what is that interest that you obtained which is 20 000 246.4 how much 70 000 to 46.4 is the amount that you would receive at the end of three years is it clear is it clear everyone the concept of compound interest guys is it clear please do respond yeah someone asked to explain again okay see uh what did happen in case of simple interest the principle did not change right it remains the same in case of a simple interest but in case of compound interest the principle keeps changing okay so how it changes let us see yeah so to start off with what is the principle 50 000 all right to start up with what is the principle 50 000 what is the rate of interest 12 percent for one year per annum means for one year so what is the interest that you get for the first year 12 on this principle which is fifty thousand so how do you get that fifty thousand into twelve pressure percentage how much six thousand correct now at the end of first year suppose had it been a simple interest will the principle change no so but here it is not the same as in case of simple interest it's going to be 50 000 the old principle plus the interest that you obtained for the first year which is 6 000. so the new principle is going to be 56 000 clear is it is it clear so far now for the second year will the rate of interest changes no it will remain the same which is 12 but the principle has changed so 12 percent has to be taken on what 56 000 so type 56 000 in your calculator into 12 how much 6 7 2 0 right clear so far okay now at the end of second year will the principle change yes it will what is the new principle old principle is 56 000 plus the interest that you obtained for the second year which is six thousand seven twenty so how much is it sixty two thousand seven twenty would be the new principle for which your third year third year at end of the second year means obviously for the third year the new principle is 62 720 now rate of interest again will it change no rate of interest will remain the same what has changed the principal has changed now what do you do 62 720 into how much percent 12 percent so what is the interest for the third year 7 000. 526.4 so this is the interest that you get for the third year now if you want to find total interest what is it you just have to add these interest three interest so how much it is 20 000 240 6.4 suppose if you want to find the total amount that you get at the end of three years it is whatever you invested that is fifty thousand plus the total interest how much is total interest twenty thousand two forty six point four and that makes it seventy thousand seventy thousand two forty six point four so that is the amount hope it is clear enough guy three is that clear shall we move on this and you are not gonna do in this method actually this is the convention and this is a the theoretical approach to find the compound interest so what is happening in compound interest you understood right principle changes at every compounding what type of compounding we assumed here yearly because principle when did the principle change at the end of first year at the end of second year right so it is yearly compounding is it clear half yearly semi-annual i mean half yearly quarterly monthly we'll see later so have you understood the concept first of all yeah everyone guys have you understood please do let me know so let's move on to the formula for ci so ci is given by p into 1 plus i whole power n minus 1 so this is the formula for c i okay let's see one by one what is p what is i what is n and all p as i mean as in case of s i it is the principle only i is the rate of interest please understand it should be a fractional value what do you understand by that if i give you 10 you have to convert this into a fraction so how do you do that 10 by 100 what is 10 by 100 0.1 what if it is one percent zero 0.01 okay please understand how to convert this into fraction let me tell you you need not use the calculator to do one what is one percent what is 1.5 percent what is 2.5 and all let me tell you how to get that quickly okay let's say if you want to find five percent all that you need to see is this percentage is a single digit or double digit number it's a single digit number right it's a single digit number if it is a single digit number if you are converting that into a fraction remember zero point zero on should be written followed by whatever number is given this is five understood suppose if it is a double digit if it is a double digit number like this then after zero point after a point you won't have another zero you will have another zero only for a single digit percentages understood if it is a double digit percentage there won't be a zero after a decimal point is it clear now 50 percent means 0.50 or 0.5 tell me 1.5 is it a single digit number or a double digit number it is single digit only right 1.5 is a single digit number only right double digit means 10 or more than 10 right now for single digit number 0.0 should be written followed by whatever given 1 5 understood what if it is 15 guys tell me what is the conversion 0.15 they won't be zero after a decimal point because it is a double digit number are you understanding are you following this everyone so the importance of this is what you do instead five percent means five divided by 100 you will you'll waste a lot of time there so instead of that if you remember these results it will be easy for you to do the calculations guys understood understood everyone online students yeah okay so i is rate of interest remember it's a fractional value so yeah what is ci p into 1 plus i whole power n minus 1 so what is n here n is number of compoundings or number of conversion periods so guys compounding means what change of principle number of compoundings means how many times the principle changes that is what is number of compounding what is what do you mean by compounding change of principle if i say number of compounding how many number of times the principle changes that is what is number of compoundings or number of conversion periods you understood and please understand number of compoundings doesn't mean it is number of years number of compounding doesn't mean number of years yes if it is annual compounding then number of compoundings and number of years is the same suppose if it is annual compounding how many times the principle changes in a year only once if there are five years the principle is going to change five times understood only for annual compounding n that is number of compoundings will be same as number of years if it is halfway compounding in a year how many times the principle changes two times two times right half really means one once in every six months right so obviously year has two such parts right so how many times the principle is going to change two times in a year what about quarterly compounding four times the number of years right we'll do the conversions later so have you understood this guys and one more thing this calculations should be done in one step in the calculator tell me guys you know the priority of doing the calculation what is the first thing that you should be typing within which bracket the smaller brackets okay so let's say for example i is two percent tell me the fractional value of two percent 0.02 guys please listen to me carefully first what is the first thing you are supposed to type 1 plus i right within the brackets the smaller bracket so don't use calculator to add 1 plus 0.02 don't add calculator to add 1 plus i why because what is i value 0.02 for example let's say if you add 1 to it where 1 gets added to the left of the decimal correct where 1 gets added to the left of the decimal when you add 1 to 0.02 it will become what 1.02 so do you need a calculator for that don't use calculator to add 1 plus i straight away since you know i value 0.02 if you add 1 to it 1 will be added to the left of the decimal it'll become what 1.0 straight away you can type the value 1.02 in the calculator and raise the power to n you know how to raise the power to n press into keep pressing equal until the counter number is n plus 1 if the power required power is 5 the counter number should be how much 6 then do what minus 1 then do what into p that's it if you do this you can get the answer in one step in the calculator itself you need not write anything on the paper everyone understood we'll be doing a lot of calculation only uh now only i'm saying how to do the calculation you need not write anything on the paper am i clear am i clear yes shall we move on shall we move on everyone please do let me know is it clear so c i is p into 1 plus i whole power n minus 1 yeah let's see the formula for amount guys tell me what is amount formula for s i p plus s i here it would be a is equal to p plus c i let me tell you how we get the finalized formula for amount guys see here what is ci formula already i have written over here what is it p into 1 plus i whole power n minus 1 isn't it i've just substituted for c i now if i remove the brackets p into 1 plus i whole power n will be as it is p into 1 plus i whole power n all right then p into 1 is p plus into minus is minus p into 1 is p all right now what will get cancelled plus p and minus p will get cancelled and therefore you get a is equal to p into what 1 plus i whole power n so this is a very very important formula formula for amount in case of compound interest also called as appreciation formula this is called as appreciation formula because derivation part is not required only remember a is equal to what p into 1 plus i whole power n you understood how we got this everyone everyone have you all understood and this formula is called as what appreciation formula also called as amount formula for compound interest and based on that they ask questions very frequently okay sometimes based on this formula only five questions were asked based on this formula only five questions were asked okay so very very important it is so only thing is that you know you have to do the conversions conversion in the sense what happily compounding what what is the conversion and a semi-annual quarterly compounding what is the conversion monthly compounding what is a conversion for that i'm going to give it in the next will be use the last formula directly yes exactly so you're supposed to use the last formula directly to find the yes that's what i meant should be using a so derivation part is not required only this amount formula and ci formula that's what is required all right shall we move on shall we everyone okay now types of compoundings and corresponding conversions because uh in compound interest problems the conversion matters no there are eight types right here only three to four types that's it not more than that okay now types of compoundings i said okay there are different different types of components like early compounding is that halfway semi-annual and monthly compounding so how to do the conversions okay so yeah for each type of compounding let's see the conversion okay it's first of all uh to start off with annual compounding so what you will be needing is you'll be in need of n and you will be in need of what i right because for the calculation you need n and you need i also right if you want to find ci or amount you need n and you need i basically what does n means n means what number of compoundings or number of conversion periods i said already number of compoundings will be same as number of years for what type of compounding yearly or annual compounding so in place of i what we can write same as number of years in place of i guys if the number of compoundings is same as number of years whatever is the rate of interest per annum given entire rate of interest is applicable right see uh i gave an example of 50 000 right 50 000 invested for three years rate of interest is 12 per annum so since it is annual compounding when the principle is going to change at the end of one year so entire twelve percent will be applicable for one year yes or no twelve percent on fifty thousand is six thousand correct but suppose if the compounding happens once in half year instead of one year if it happens in once in half here tell me will the entire 12 percent per annum is applicable for as the interest no why because it is only for half year one year it is 12 percent half here is obviously six percent so six percent on fifty thousand calculate three thousand now what is the new principle at the end of half year fifty thousand plus three thousand which is fifty three thousand now for the next half year again how much percent six percent or twelve percent six percent so you understood for half yearly compounding the interest that is applicable is how much half of the given interest you understood everyone guys you understood this so how much is applicable for halfway compounding whatever the rate of interest per annum they give you only half of that so it is how do you write that interest rate per annum by two now if you have understood this conversion for annual compounding you should be able to do the conversion for semi-annual compounding very easily tell me number of compoundings tell me in one year how many compoundings will happen semi-annual means two compoundings will happen can i write two into number of years suppose if there are four years let's say how many times the principle will change once in a year i mean twice in a year if there are four years of investment 2 into 4 which is 8 times the principle is going to change so can i write in general n is equal to 2 into number of years why 2 we have because in 1 year principle is going to change two times so if there are n number of years if there are number of years let's say it could be four it could be five it could be even six also so two into number of years we can write generally yes or no you understood so tell me oh sorry i wrote what why did i write 4 divided by 2 for the first one i explained that for halfway compounding right so this should have been what it's just the interest rate per annum yearly compounding entire rate of interest is applicable so n is equal to number of years for annual compounding i will be equal to same as interest rate per annum for what type of compounding annual compounding for semi-annual compounding i will be what interest rate per annum divided by what how much is applicable only half of the total interest so it will be divided by 2. all right now tell me for quarterly compounding what is n 4 into number of years why 4 into number of years because in a year the principle is going to change four times now tell me interest will be how much by four because half yearly means it gets divided by half quarterly means in a year four times the principle is going to change only one-fourth of the total interest therefore i will be interest rate per annum divided by what four so if you've understood so far you should be able to do it for monthly compounding tell me what is n 12 into number of years what will be i interest rate per annum divided by 12. so these conversions has to be taken care of first then you substitute that in the formula in one step guys have you all understood the conversions have you understood the conversions yes for annual compounding interest rate per annum is same as i is same as interest rate per annum only so for semi-annual since i was explaining about seminal compounding i wrote that divided by 2 it was for semiannual compounding right so whatever the rate of interest they give you for annual compound i mean in the question the same will be the rate of interest for annual compounding and tell me i should be always what fractional value or a percentage value it's always a fractional value is that clear everyone everyone clear shall we move on okay now let's see the problems on ci guys please understand whenever you get up questions on population is it a compound growth or a simple growth how do you say compound growth let's say today's population is one lakh and the growth of population is five percent every year let's say at the end of one year the population will become one lakh five or five thousand then next again five percent five percent and what is it one lakh or one lakh five thousand one like five so it's a compound growth right so whenever you get a question on comparing uh the population always it is com compound compound interest only okay they need not specify it as as per ci so you need to understand it as compound growth only so you have to apply the concept of ci only is it clear so guys for compound problems on ci the simple problems on ci you need to know two basic formulas what are those basic formulas ci what is it p into 1 plus i whole power n minus 1 and the other one is appreciation formula that is a is equal to p into 1 plus i whole parent so problems based on these two formulas only right shall we move on shall we okay so let us see the first type of a question the first type of equation is a straight question you will be given time you will be given rate of interest you will be given the principle you will be asked to find ci or amount same like type one question of simple interest okay to find ci problems on ci and a given what p i and n p i and n will be given to you you'll be asked to find what ci or amount shall we see the questions everyone shall we see the questions okay now look at the question what is principal 30 000 what is the rate of interest 12 percent per annum and time is three years and look at the questions first of all for annual compounding you have to calculate what ci and amount both first of all guys i'm solving the first sub question annual compounding tell me for annual compounding what is the conversion n will be same as number of years what is the number of years they have given three i will be same as interest rate per annum that is 12 12 or 12 percent so would you write a percentage value or a fractional value so what is fractional value of 12 percent 0.12 so this is the conversion for what annual compounding we want it for semi-annual also correct semi-annual tell me the conversion for semi-annual n will be 2 into number of years that is 2 into 3 which is 6 i will be interest rate per annum is 12 that is 0.12 divided by what 2 and the result is 0.06 correct 0.06 so and the third one is quarterly what is n 4 into number of years that is 3 which is 12 and what is i 0.12 divided by 4 which is 0.03 and finally for monthly what is n 12 into 3 which is 36 and i will be 0.12 divided by 12 which is 0.01 so we got the conversions for all the compoundings now what we need to calculate for the first one ci what is ci p into 1 plus i whole power n minus 1 right this is uh ci now tell me what do you do first of all 1 plus i guys we are finding it for annual compounding first of all so i value is 0.12 means what is 1 plus i would you use the calculator to do 1 plus i no 0.12 when 1 is added to it it will become 1.12 straight away type 1.12 in the calculator raise the power to what what is n for the angle compounding 3 how do you raise the power to 3 press into keep pressing equal until 4 appears as a counter yes then what you do minus 1 right then we are done everything within the square brackets then come out of the brackets it's a multiplication right into p what is p 30 000 and the result of it twelve thousand one forty seven point eight four so what will be amount add principle to it that's it anyway ci is there in the calculator add principle to it what is principle thirty thousand thirty forty yeah 42 000. 42 000 140 2000 147.84 just add a principle to it you get a amount so similarly can you tell me what is ci for the second one you need not write the formula already formula is there right what is one plus i for this semi-annual compounding 1.06 correct 1.06 is 1 plus i raise the power to what 6. how much is ci 555. five seven what is amount i had thirty thousand to it forty two thousand five fifty five point 55.57 how about the third one so ci formula is right here what do you feed first of all 1 plus i i is what 0.03 when you add 1 to it it will become 1.03 raise the power to what twelve twelve thousand seven seven point five twelve thousand seven seventy two point eight two guys online students i'm not getting answers from your end please do it for monthly also guys are you getting the answers or should i explain again the calculations please tell me getting the answer explain the calculation again how about others about others okay listen let me explain the have you understood the conversion first tell me have you understood the conversion for each type of compounding everyone yes now listen to the calculation so what is ci p into 1 plus i whole power n minus 1 all right p into 1 plus i whole power n minus 1 what is the first thing that you have to type whatever within the smaller brackets for first here first one means what annual compounding look at the conversion in annual compounding i is 0.12 when you add 1 to it don't use calculator to add 1 to 0.12 straight away you can write down what 1.12 because when you add 1 to 0.12 it will go to the left of the decimal it will become what 1.12 what you should be typing straight away in the calculator 1.12 how do you raise the power to n what is n for the annual compounding 3 press into keep pressing equal until the counter number is one more than three that means four okay what do you do after that minus one all right then into p press into button type p what is p thirty thousand so how much is the value you're getting twelve thousand twelve thousand fourth one is correct yeah so have you got the answer now no no uh yeah ramya you got the answer now yeah what is ci for the fourth one twelve thousand nine twenty three point zero six and amount is forty two thousand nine twenty three point zero six tanya listen to the calculations so which one you want me to do uh annual semi-annual quarterly or monthly which one which one annual fine listen listen so you understood the annual compounding i want you to respond at each and every point you understood the annual compounding conversion yes now what is asked ci and the amount yes what is asked ci and the amount you know ci formula is p into 1 plus i whole power n minus 1 yes yes okay so according to the priority what is the first thing that you would type whatever within the smaller bracket that is one plus i correct so i value is right here for annual compounding 0.12 clear now when you add 1 to it do you use calculated to add 1 to 0.12 don't use it ok so when you add 1 to 0.12 it will go to the left of the decimal point it will become what 1.12 clear respond clear okay now have you typed 1.12 in the calculator type it 1.12 all right now you have to raise the power to n what is n for annual compounding 3 that means what press into keep pressing equal until the counter number you can see the counter number as 4. you have to keep pressing equal until you get the counter number as 4 so you get some value right for 1 plus i whole power in yeah you got some value then what are you supposed to do minus 1 minus 1 okay done with that then come out of the brackets what is there out of the brackets p what you have to do if there is no sign between the two variables into you have to do press into button and type what p what is p 30 000 now tell me what is the value you are getting twelve thousand one forty seven point eight four you understood understood and listen we are not it done since we have to find even amount also guys you got this interest you add principle to it you get the amount yes or no don't again use the formula of amount a is equal to p into one plus i whole current it's a waste of time already we have a ci in the calculator right just add what principle to it what is principle thirty thousand what do you get forty two thousand one forty seven point eight four sure sure we'll do semi annual once again no problem listen semi-annual compounding what is the conversion n is 2 into number of years which is 6 and i is 0.12 is interest rate per annum divided by 2 which is 0.06 yeah is it fine with the conversion everyone the conversion is clear the conversion is clear okay now come back to the formula now what is the first thing you are supposed to type 1 plus i value correct so what will be 1 plus i i want you to respond what will be 1 plus i look at i value 0.06 what will be 1 plus i what is it so here what will be 1 plus i 1.06 yes type 1.06 in the calculator please don't use calculated to add 1 plus 0.06 straight away in the mind 1.06 okay raise the power to what 6 n is 6 right how do you raise the power to 6 press into keep pressing equal until 7 appears as a counter number all right then what you do minus 1 okay then into p you just have to follow the priority that's it okay just follow the priority so how much you're getting now how much you got 12 seven of 555 yes and to find the amount what you do add thirty thousand principle to it you get forty two thousand five fifty five point seven is that clear now is that clear everyone is that clear okay right so conversion is the key before typing one plus i i value you have to see an n value you have to see depending upon the type of compounding then only you have to substitute in the calculator am i clear so far everyone okay let us move on to the second example a time by which a sum of money would triple or double itself at five percent per annum ci guys had it been si question which type it would be suppose if they say as per si instead of ci if if there had been s i which type it is seventh type but unfortunately this is not si this is ci you can't apply type 7 of si for this because clearly they have specified it is as per ci please don't get confused you have to so i said you have to look at the question whether it is s i or c i don't apply s i concepts to c i why you can't apply in case of sr principle doesn't change in case of c principle will change so you can't be applying the same concepts here also am i clear everyone okay guys what do you understand double means what a is equal to a is equal to 2p double means what amount is equal to twice the principle is it clear is it clear everyone what is the question asked time in how many years it will become what double so let me show you the options 14.2 years 14 years 12 years and 15 years okay let's listen here by looking at the question it is double means a is equal to what 2p correct this amount and principle are related tell me which formula in case of compound interest relates amount and the principle which formula relates amount and principle what is that formula called as which formula connects amount and principle in case of ci what is that formula appreciation formula what is it p into 1 plus i whole power n now what do i substitute in place of a 2 p 2 p is equal to p into 1 plus i guys i is 5 means 0.05 correct now have this specified the type of compounding here no if they don't specify the type of compounding default it has to be taken as annual compounding only if not specified default compounding is annual okay now guys in place of 1 plus i what do i write 1.05 whole power what n now p and p cancels so you should be getting 2 is equal to 1.05 whole power n now what is that we need to calculate according to the question n right n is what we need to calculate let's tell me which is the moderate option in the given options 14 is the moderate option yes or no 14 is the moderate option so you can do it by option hitting type 1.05 in the calculator keep raising the power up to 14. 14 means the counter number should be what 15 the counter number should be 15 for power 14. so what is the value you're getting you should be getting 2 but you're getting 1.97 for 14 but 14 is the lesser value you have to go for the higher option check for 15 now check for 50 it's it's little more right so obvious option should be 14.2 years have you understood for 1.97 it is little less for uh 2.07 it will be more so obvious option is 14.2 years have you understood have you all understood if you plug in n is equal to 14 you get 1.97 but what you must be getting here 2 if you plug in n is equal to 15 you will be getting how much 2.07 it is greater than 2 correct so obvious option is 14.2 once again ah i'll tell you i'll tell you you can't find out 14.2 but you can find out 14.25 i'll explain that don't worry okay guys look at the question first of all a time by which a sum of money would double itself what do you understand by sum of money doubling a is equal to 2p is this point clear everyone please tell me please respond is this clear a is equal to 2p how we wrote a is equal to 2p because they say doubles and guys please do respond i want everyone to respond at any point if i ask is it clear yes okay right so a is equal to 2p which formula connects amount and the principle as per ci appreciation formula what is it p into 1 plus i whole power n correct now what do i write in place of a because a is equal to 2p for double what do i write in place of a 2p correct p into 1 plus i i value is 5 means 0.05 so what will be 1 plus i 1.05 whole power n is it clear so far tell me everyone online students also please tell me is it clear so far yes okay now what will get cancelled 2 p and p will get cancelled so what you must be getting is 2 should be equal to 1.05 whole power n all right now you have to plug in the options okay guys the moderate option here is 14 by plugging in n is equal to 14 what is the result of this 1.97 but 2 is greater than 1.97 so now n value has to increase or decrease it has to definitely increase then only this value would increase yes or no by plugging in n is equal to 14 you get uh the result of one plus 1.05 whole power 14 as 1.97 so the value is lesser than 2 now if you think of 15 by plugging in n is equal to 15 now tell me press equal to one more equal to see anyway you have 2 power 14 right press one more equal to you get for 15. how much it is 2.07 this is lesser than i mean 2 is less than 2.07 what we are looking for is 2 exactly so definitely that value will lie between 14 and 15 so the only option is 14 point you understood now everyone see by plugging in n is equal to 15 you get 2.07 by plugging in n is equal to 14 you get 1.97 tell me for which value this result is very closer to 2 is 1.97 close to two or one two point zero seven close to two one point nine seven is very close to two that means it should be close to fourteen point two i mean fourteen very close to fourteen that means fourteen point two should be the answer guys i told you you can't find out for 14.2 you can find it out for 14.25 let me now tell you how to find it for 14.25 how to raise the value of power of a number to 14.25 or anything 2.25 or 3.25 first of all i'll explain how to raise the power of a number to 0.5 to 0.5 let's say you have to find 2 power 0.5 how to raise please understand can you raise the power to 0.5 in the calculator no but look at this 0.5 can be written as 1 by 2 what do you mean by any number whole power 1 by 2 square root of that number square root of that number now let me tell you suppose had it been 2 power 2.5 can you raise the power to 2.5 no but 2 power 2.5 can be written as 2 power 2 into 2 power 0.5 bases are same they can be added so 2 power 2 is 4 and this is root 2 correct so this is how you can find out 0.5 values now let me tell you suppose if you have 2 power 1 by 4 or 0.25 guys what do you mean by 0.25 1 by 4 please understand whole power 1 by 2 means what square root whole power 1 by 4 means square root twice press the square root square root how many times twice so for 0.25 what you do the base number your type press the square root how many times two times now now let me tell you how to get for 14.25 you understood 0.25 means what whole power 1 by 4 whole power 1 by 4 means what that number square root how many times 2 times all right now listen so for 14 we did not get 2 exactly now 14.25 1.05 whole power 14.25 how do you split this 1.05 whole power 14 into what 1.05 whole power 1 by 4.25 means what 1 by 4. guys already we have 1.05 whole power 14 how much one point nine seven nine seven or nine eight check ones is it nine seven or nine eight nine seven nine nine so that means approximately nine eight right one point eight now what you do type 1.05 in the calculator press square root how many times 2 times then into what this value already we have 1.98 how much for whole power 15 only you're getting 2.07 how come it will be 2.10 two point double zero four so is it very close to two compared to these values so for 14.25 you're getting approximately equal to to the closest answer to this is 14.2 years but is it actually required to do this no for 14 you get just lesser value for 14 15 you got more than value obviously the correct answer will be between 14 and 15. so 14.2 is the right answer so since you asked i told you how to check 14.25 in the calculator guys have you understood online students have you understood please tell me if you have any issues with it because the calculation is important thing okay have you all understood how it is 14.2 why not it is 14 why not it is 15 yeah for 14 you get just less than 2 for 15 you get little more than 2 so obviously the answer will be between 14 and 15 the only option that is there in the given one is 14.2 clear everyone shall we move on shall we guys shall we move on yes so how do you say for n is equal to 14 1.05 whole power 14 is 1.98 approximately for n is equal to 15 1.05 whole power 15 is how much 2.07 therefore n should be equal to between these two which is 14.2 55 yeah okay let's look at the next question in what time will rupee 1000 amounts to rupees one lakh twenty six thousand six seventy seven at six percent per annum when the interest is compounded semi-annually guys what type of compounding semi-annual tell me for semi-annual compounding what is the conversion what into number of years 2 into number of years so how many years they have given here that is what they have asked right 2 into number of years and they have given an information right 1.03 whole power 8 is equal to 1.26677 all right right so what is what is i for semi-annual compounding guys interest rate per annum is 6 percent mean 0.06 divided by what 2 that means 0.03 yes yes yes look at the fun in this question look at the fun in this question don't you think this is one plus i whole parent whatever the given information there whatever the information they have given don't you think this is one plus i whole power n what is i we got 0.03 plus 1 is 1.1.03 that is nothing but 1 plus i only so what is 8 n is equal to no n is equal to 8 but what is n for semi-annual compounding equity to what two into number of years now tell me guys what is number of years four years so do we have to use principal and amount to solve this question actually not have you understood once again okay guys have a look at this question they've given what type of compounding semi-annual compounding for semi-annual compounding semi-annual compounding what is the conversion n is equal to 2 into number of years all right and what is i interest rate per annum is 6 percent that is 0.06 divided by 2 which is 0.03 if you look at the given information 1.03 means 1 plus i only what is i 0.03 when you add 1 to it will become 1.03 and what is this 8. so the given information is basically what 1 plus i whole power n 1 plus i whole power n given in the question is 1.03 whole power 8 so comparing what is n equal to 8 but it is not a yearly compounding it is semi-annual compounding for semiannual compounding what is n 2 into number of years you have to equate that to 2 into number of years now this two ones are two fours are the number of years equal to what suppose if they don't give you this information what do you do principle and amount both are given which formula would you use compound interest appreciation formula use that formula and do it that's it have you understood have you understood but is it required to use that formula and solve this actually not because they have given off the the value of one plus i whole power n by comparing n is equal to how much eight but is it number of years no because n is two into number of years for semi-annual compounding had it been yearly compounding it would have been eight only eight years only since it is semi-annual compounding n will not be number of years it will be two into number of years so eight is equal to two into number of years therefore number of years will be eight by two which is four years have you understood everyone everyone online students can you solve using appreciation formula please we can do it listen a is suppose if they don't give you this value okay how to solve this a is equal to p into 1 plus i whole power n all right now what is a 1 lakh 26 000 677 what is p 1 lakh so where will this p go to the denominator of lhs or divide one lakh 26 000 by 1.2667 what remains on the right side 1.03 whole power n correct point zero three whole power n yes or no you understood this so far y zero was it a one point zero three because semi-annual compounding i is not six percent it is going to be three percent so it's going to be 1.03 whole power n now all that you need to do type 1.03 in the calculator press into keep pressing equal until you get this value 1.2667 and tell me the counter number counter number is nine but actual value is one less than that which is eight okay but is it number of years no what is n for semi-annual compounding 2 into number of years all right therefore number of years equal to 8 by 2 which is 4. so this is how you can solve by conventional method if they don't give you it's compounded the component early means do we have to take n s number of years exactly answer would be eight suppose if they give you number of i mean compounding as annual compounding n will be same as number of years is it clear have you all understood clear so far please tell me shall we move on shall we move on guys okay yes let us solve this question a sum of money compounded annually becomes eight thousand four fifty in how many years two years and rupees ten thousand nine eighty five in how many years three years okay how many amounts are given two amounts that means don't you have two cases here two cases okay what is a in the first case eight thousand four fifty what is appreciation formula p into one plus i whole power what type of compounding have they mentioned have they mentioned no if they don't specify n will be same as number of years so how many years they have given first case two years so let me call this as equation one all right second case a is equal to what i'll write a1 a2 10985 is equal to p into what 1 plus i whole power 3 call it as equation 2. clear is it clear so far now guys there are two equations and two unknowns no if you want to cancel p what do you do multiply divide subtract what you do array divide by dividing only p gets cancelled right yes or no two by one or one by two two by one if you do two by one if you do two by one guys tell me the left hand side value ten thousand nine eighty five divided by eight thousand four fifty how much one point three and that is equal to guys one plus p p cancels to one plus i all power three divided by one plus i whole power two correct power two power 2 cancel how much is remaining power 1 is remaining so 1.3 is equal to what 1 plus i what is that we are asked to find i value right where will this one go on the other side so 1.3 minus 1 is 0.3 so i is equal to 0.3 therefore 30 percent understood understood everyone is it clear please tell me guys is it clear once again okay okay this is as per ci any doubt what says it is as per ci clearly they have specified what compounded annually so it is a compound interest why it is 2x1 okay i'll tell you listen see in the first case amount is how much i'll write a1 8450. what is the amount formula p into 1 plus i whole power n in the first case how many years they have given 2 so i would write 2 that is equation number 1 okay second amount is how much ten thousand nine eighty five which is equal to p into one plus i in how many years they have given three years this is equation two so yeah since you asked why equation two by equation one have a look equation 2 has got more amount compared to equation 1. and why are we dividing basically if you divide it p and p get cancelled yes since we are dividing what happens p and p gets cancelled you can find the value of i that is asked in the question right so why it is equation 2 by equation 1 you understood now if you do equation 2 by equation 1 the left hand side expressions will get divided that is 10 0985 by eight thousand four fifty how much it is one point three and that is equal to one plus i all power three in the denominator this value one plus i whole power two all right now power 2 cancels with power 2 how many powers are remaining only one power is remaining that is 1.3 is equal to 1 plus i clear so what is finally we need to calculate i value so i value is 1.3 minus 1 is 0.3 what is 0.3 means 30 percentage so the answer for this question is option a now guys the same problem can be solved in one more way but there should be some identifying factor for solving that question in one more way please understand what is the number of years difference between these two cases one is two years the other one is three years if the difference between the two years given in the question is one year and if they give you two amounts in the question as per ci please understand you can solve it by type 3 of simple interest by considering the first amount as principle second amount as amount only this is p and this is a you can solve it by what type three of simple interest why it is so listen please try to understand try to understand yes if you invest 10 000 rupees at percent per annum uh let's say ten percent per annum as per ci as per ci tell me to begin with what is the principle ten thousand at the end of one year what is the interest that you get for the first year one thousand rupees correct the principal at the end of first year will be what 11 000 correct now guys listen the concept is very simple suppose if you withdraw your amount at the end of first year what is that you get eleven thousand eleven thousand is basically what amount isn't that the principle for the second year the amount at the end of first year is same as the principle for the second year or the amount at the end of second year is the principle for third year understood so this is the amount at the end of two years this is the amount at the end of three years so this amount at the end of two years is the principle for which your third year so you can consider that as p this is a and you can solve it by using which method type three what is that we are asked rate of interest that is r what is it a minus b divided by p into t into 100 but please understand here t should be what difference between the two time durations that is one you want to take it as one difference between the two dimensions please do the calculation what is a 10985 minus what is p 8450 divided by what is p 8450 again divided by you need not do it by one okay because t is one into hundred how much percent thirty percent we'll solve it conventionally also we'll solve it using this method also yeah sean shortshaw please take down the note for that please take down a note if the difference between difference between the two time durations time durations is one year then the first amount can be taken as what can be taken as p and second amount as a and then the same question the question can be solved question can be solved using what type using type 3 of of si only for difference in time duration being one year you can't do it for two years and three years understood you can't do it for two years or three years look at the second problem what is the time duration difference one year only it is one year only so you can solve this by type 3 of simple interest by taking the first amount as p second amount as a so what is the answer 20 is it clear is it clear everyone so you have to identify right if the difference between the uh two time durations is one year and then they give you two amounts as per ci then take the first amount as principle second amount as a then solve the question by type 3 of simple interest otherwise you'll have to solve it this way which way the the way which i explained earlier using compound interest only you can solve it you understood you understood everyone guys please tell me is it clear online students no response yes is it clear any doubts please do ask shall we move on so should i write type 3 form shortcut formula not required right a minus b divided by b into t whole multiplied by hundred t must be taken as one t is equal to one for this kind of problems right shall we move on okay now type 2. to find a when p and different rate of interest for different years are given this is type t o type 2 of compound interest so what is that we need to calculate amount when principal and different rate of interest for different time durations are given is first of all tell me what is amount formula for compound interest p into 1 plus i whole power n okay please concentrate here then you can copy it later just listen to me okay see guys suppose if i plug in n is equal to 3 okay assuming annual compounding only assuming annual compounding and n is equal to 3 if you plug in it has 1 plus i whole power 3 don't copy this only if you're understanding i'm saying can i split this as 1 plus i into 1 plus i into 1 plus i because it is whole power 3 can i split it yes or no yes is it clear guys everyone online students also please tell me is this clear i've just taken n is equal to 3 okay and i have splitted p into 1 plus i hold power n is p into 1 plus i into 1 plus i into 1 plus i guess here the rate of interest are same or different ah i i i it's the same so why we are able to write 1 plus i whole power 3 right since the rate of interest for each and every year is the same so why we are able to write 1 plus a whole power 3. now what are we looking for here different rate of interest for different years okay so if the rate of interest are different for different years in place of first i it is i1 second i it is i2 the third eye is i3 that's all you need to do how do we obtain this formula tell me from the appreciation formula only we expand the appreciation formula to obtain the formula for amount when the rate of interest are different for different durations have you understood have you understood here number of years sir into a 1 plus i i 4 into one plus i they will not give you for 10 years yet so if they give you for ten years how big the question is going to be rate of interest for the first year is five percent for the second year it is ten percent for the third year it is fifteen percent they can't be asking they can ask only for three years or maybe maximum four years not more than that guys is it clear how we get the formula a is equal to p into 1 plus i1 into 1 plus i2 into 1 plus i3 and so on so how did we get this formula tell me you want the base for this a is equal to p into 1 plus i whole bar n ok so this can be splitted as what p into 1 plus i into 1 plus i and so on right shall i right so on for your understanding i took only n is equal to 3 so why i wrote only three terms so the rate of interest are different in place of each i i would write i1 i2 i3 and so on understood understood so do you have to just you have to by heart this it's not required if you know appreciation formula you can easily get the formula for rate of interest being different is it clear everyone online students is it clear yes yes okay right shall we look into the problems yeah the present population of a town is 70 000 what do you know know about this what do you say about this what is this actually present population of a town is 70 000 means principle or amount principle today's value right so this is p if it grows at four percent five percent and six percent per annum for the first second and the third year respectively then find the population of the town at the end of three years so what is that we are asked to find population at the end of three years means amount of what it's amount only right so we need to calculate a what is the formula that connects a mountain principle as per see is it as per ci population always it is as per ci even though they have they haven't specified whether it is ci or s i population problems are always ci based all right so a is equal to p into 1 plus i 1 into 1 plus i 2 y this formula tell me rate of interest are different so b into 1 plus i 1 into 1 plus i 2 how many durations they have given 3 right 3 years 1 plus i 3 guys that's all for your reference no need to write anything on the paper why because what is i one four percent that means zero point zero four what is one plus zero point zero four one point zero four type what one point zero four into what one point zero five into what one point six into what principle and the answer is 26.4 understood don't substitute values guys what i 1 four one plus i one is one point zero four into i two is zero point zero five so one plus i two will be zero point one plus one point zero five i three zero point let me write it okay this is zero point zero five this is 0.04 all right so feed the values 1.04 into 1.05 into 1.06 into what principle which is 70 000 and that gives you the answer as 81026.4 have you understood everyone have you understood please do respond understood please do ask me if you have any doubts don't keep any doubts in your mind right clear how about tanya ramya got the answers yes what no population is always ci okay understood yeah okay uh we'll do one more problem on type two please take down one more example okay a certain sum of money sum of money amounts to amounts to rupees say 12 500 at the end of at the end of three years as per ci okay if the rate of interest if the rate of interest are eight percent comma nine percent and twelve percent per annum for first three years first second and third years find the sum [Music] uh what is the question asked find the sum means what principle you need to calculate what is this 12 500 amount what do you do among you type first what is amount 12 500 this one plus i1 will go where denominator divided by 1 plus i1 first correct yes you understood what it is amount is given twelve thousand five hundred divide the amount by one plus i one first what is one plus i one one point zero eight again divided by one plus i2 1.09 again divided by 1 plus i3 which is 1.12 and the answer is [Music] 9480.72 guys understood understood why are we dividing because p is asked so a divided by 1 plus i 1 into 1 plus i 2 into 1 plus i 3 guys i told you this kind of divisions in the calculation part right yes so don't multiply 1 plus i 1 into 1 plus i 2 into 1 plus i 3 it's a waste of time what do you do amount divided by 1.08 again divided by 1.09 again divided by 1.12 12 means 2 digit number after a point there is no 0 1 2 as it is so the answer for this question is 9 000 how much 480.72 have you understood everyone online students nice please respond this is not oh yeah what's the issue you got the answer or not you have not got the answer not got the answer listen see what is the question asked here a certain sum of money a certain sum of money amounts to rupees twelve thousand five hundred so is it amount or principle you you respond to me is it amount of principle certain sum of money means they have not given the principle sum of money how much they have not given so this is actually what amount amount is given in the previous question principle was given here amount is given what is that they're asking some so the same formula you're supposed to use but what slight modification since we need to find p where will this 1 plus i 1 1 plus i 2 and 1 plus i 3 go to the denominator of l h so that's what i've written here right so what is a in the question twelve thousand five hundred type twelve thousand five hundred please do it then press the divide by button one plus i one what is i one eight percent means zero point zero eight so one plus i one is 1.08 so divided by 1.08 first then pressure divided by again what is 1 plus i2 1.09 because this is 0.09 all right what is 12 0.12 so what do you divide now 1.12 so how much do you get you got the answer no yes you understood understood right got the difference between the two questions yes or no if you want i'll just quickly revise the three types that we discussed any doubt in any concept type of compounding if you have any issues ask me we'll do it so because this chapter is very very important in terms of mark that it carries 12 to 16 is not a smaller number you know weightage of mathematics is 40 out of 40 eight chapters are there out of 40 marks 12 to 16 from one chapter only so it's a huge weightage right so you should be getting out of out from this chapter that is only possible if you practice okay so if you practice and come when i take up the previous paper questions after completing the concepts you should be able to solve them very easily but only thing is that whatever types that we have done so far that should be there in your mind if it is that you can easily solve the questions okay then after that we will continue with type 4 okay with type 4 we are done with compound interest right only four types and literally uh we have discussed three types right so for three types three types or two types yeah two types it's actually one type only amount formula only we used to get type two same amount formula we expanded and wrote that's it right does it make any difference there there's no difference difference has only been what expansion of amount formula and just be substituted in place of each i as i1 i2 i3 that's it so based on this formula they can ask amount by giving principle or they can ask principal by giving amount if they ask amount you need to multiply everything if they ask principal amount divided by 1 plus i1 divided by 1 plus i2 divided by 1 plus i3 clear everyone [Music] yeah guys uh started with compound interest we completed two types any doubt so far please do ask me any doubts on any type of compounding please ask me if you have any doubts going forward okay so since you don't have doubts i'll ask you questions yeah shall i can i ask you questions okay tell me if a rate of interest per annum is 10 percent per annum okay rate of interest is 10 per annum for quarterly compounding what is i what is i value for quarterly compounding what is i 0.025 how do you do the conversion early compounding is 0.1 divided by what quarterly 4 answer is 0.025 right what is it if it is monthly i will be 0.1 divided by what 12. so what is it 0.0 0 0 8 3 3 yes so be very careful when you write i numerator should be kept in what decimals only okay please keep the numerator in decimal 10 percent means 0.1 divided by 12 work monthly compounding what will be n for monthly compounding if number of years is 4 what is n for monthly compounding if the number of years is 4 12 into 4 because for monthly the conversion is 12 into number of years which is 48. for semi-annual what is n 2 into 4 which is 8 number of years is 4 i've given clear all conversions clear everyone please tell me all conversions clear okay right the two uh types that we discussed was type one based on what uh ci or amount you'll be given time you'll be given a type of compounding you'll be given what rate of interest per annum you will be asked to find ci or amount using the formula ci is equal to what p into 1 plus i whole power n minus 1 tell me what is the first thing you have to do conversion is the first thing that you should do then feed what 1 plus i so if i is equal to 0.05 what is 1 plus i 1.05 raise the let's say n is equal to 10 what do you do press into keep pressing equal until you get 11 as a counter then what you do minus one okay then into what principle so you get the ci clear clear so first of all what is very important thing conversion i value n value you have to write down somewhere then plug in the values in the calculator this is type one so type one they may sometimes ask you questions on appreciation formula how do you know you have to use appreciation formula they'll ask you rupees some some sum of money is invested uh what at rate of five percent per annum after three years what will be the amount what will be the amount at the end of three years so what is that we need to calculate amount so p will be given i will be given and n will be given so you have to use what formula appreciation formula for population problems also appreciation formula only and we discussed one of the problems what is it uh certain some take one problem a certain sum of money sum of money amounts to rupees one one four zero in two years and rupees one seven one zero in three years as per ci find rate of interest guys if it is as per si which type in si type 5 but this kind of a question if you get on compound interest always look for what the two different time duration two three two years and three years difference is what one when you get the differences one apply type three of simple interest by taking this as p this is a apply type three of simple interest even though it is a compound interest problem condition is what what is the condition applied difference between the time durations must be one year for applying type 3 tell me what is that you substitute in place of t what is that you substitute in place of t t should be always 1 t should be always 1 clear everyone clear everyone guys respond is it clear yes then we saw type 2 what is type 2 rate of interest are different for different duration uh which formula by expanding you get to say the formula appreciation formula so you know appreciation formula is a is equal to p into 1 plus i whole power and that can be splitted as 1 plus i 1 plus i and 1 plus i so on since the rate of interest are different you will write i1 i2 i3 if they ask you amount this is what you have to do if they ask you principle p is equal to a divided by 1 plus i1 1 plus i2 and 1 plus i3 we solved both the varieties right if they give you principle they'll ask you to find amount they give you amount they'll ask you to find the principle clear clear everyone guys please do respond is it clear yes we'll move on we'll move on to type 3 observe type 3 it's similar to type 4 of a simple interest is it not two amounts in terms of principle isn't it and the time in the first case given and to find what time in the second case similar to what type 4 of simple interest but the only difference is what that is as per si this is as per ci okay let's see so is there any difficulty for you to identify two amounts in terms of principle guys is there any difficulty for you to identify two amounts in terms of principle how do you identify double triple four times five times if you get some amount if you get amounts like this it is always amount in terms of principle how many amounts you have to find two such amounts in the question the moment you see such two amounts it is in case of uh ci it is type three in case of s i it is type four okay oh sorry guys look at the question a certain sum of money doubles itself in four years as per ci in how many years and very important thing that you have to notice is what this is as per ci this is the point that says it is not type 4 of simple interest it is type 3 of compound interest is it clear otherwise it's same right in how many years it will become 16 times the sentence formation everything is same as what type 4 of simple interest the only thing that says it is compound interest is what as per ci guys don't you have two cases here so we're going to solve this in conventional method however we did for simple interest so there are how many cases here two cases what is case one guys a is equal to what p double means a is equal to two b second case a is equal to 16 b here guys is it clear so far now a is equal to 2p now relationship between amount and principle this is as per ci what is the formula that connects amount in principle in case of a appreciation formula what is it a is equal to p into 1 plus i whole power n what is n here have this specified what type of compounding here no if they don't specify by default annual compounding okay so why in place of n i wrote 4 only now what do i write in place of a 2p is equal to p into 1 plus i whole power 4. what gets cancelled here p p cancels and you get 2 is equal to 1 plus i whole power 4. clear clear now we do the same thing further i mean i'll call this as equation 1 okay i'll do the same thing on the for case 2 also right so what is it a is equal to p into 1 plus i whole power n we don't know what is n we know what is n for case 1 we don't know what is n for k 2. so i'm writing n only what do i write in place of a 16 p is equal to p into 1 plus i whole power n all right now we have pp on both the side we can cancel it and we have what 16 is equal to 1 plus i whole power n guess we have got two equations right how do you get rid of n and i it's not possible right is it possible to solve this no what we can do here is what we can do here is can i write 16 in terms of 2 if so how do we write 16 in terms of 2 2 power 4. so i can write 16 as what 2 power 4 and that is equal to 1 plus i whole power and why i express 16 in terms of 2 because i know what is 2 is what is 2 1 plus i whole power 4 so if i substitute 1 plus i whole power 4 is 2 but 2 has got a power what is it 4 right whole power 4 and that is equal to 1 plus i whole power what what n n i mean on the right side yeah now what is it one plus i whole power four fours are how much 16 is equal to one plus i whole power n guys by comparing by comparing bases are same you can equate the powers so which implies n is equal to how much 16. how much time it will take one minute two minutes it will take so i mean this this this point should strike your mind how do i solve next right if you don't express 16 as in terms of four can you solve this further definitely not if this doesn't come to your mind you can't solve this question so this is the conventional method could you please explain the last part yes i would do that uh from where or should i shall i do it from the beginning or okay all right last part i'll do it again yeah okay so you understood equation one and equation two up to that you understood everyone equation one and equation two have you all understood yes everyone please do respond yeah now see we have got two equation here uh sorry yeah 1 plus i whole power 4 is there but here 1 plus i whole bar n right i is the unknown and even n is the unknown we can't cancel i or n right it is not possible to cancel that so what instead you can do is substitute 16 in terms of 2. how do we write 16 in terms of 2 2 power what 4 2 power 4 is 16 right and that is 1 plus i whole power n now guys do we have a substitution for 2 what is 2 1 plus i whole power 4 so in place of 2 we can write what 1 plus i whole power 4 1 plus i whole power 4 but 2 has got a power how much that has to be raised yes or no whatever substitution we have made is only for 2 right since we have 2 power 4 that power has to be raised yes and that is equal to what 1 plus i whole power n now if you see except 1 plus i the powers 4 and 4 is there always the powers get multiplied so you get 1 plus i 4 4 how much 16 is equal to 1 plus i whole power n is it clear so far now the basis on both the sides are same the powers can be equated so what is n equal to n is equal to 16 years you understood everyone is it clear but you need not solve in this method i'm going to give you the shortcut for this yeah are you ready for the shortcut everyone you understood the conventional method there are two amounts in this question a is equal to 2p and a is equal to 16b sorry in terms of what guys these are all in terms of what principles yes or no this is cs1 a is equal to 16 b so there are two amounts in terms of principle as per c it is so this is what you do in conventional method now we'll see in a shortcut right you can't apply that shortcut of simple interest here so please don't mix up simple interest we are done now compound interest it's a different approach because how simple induce and components are different in what sense principle doesn't change in case of s i principle changes in case of ci so that's the differentiating factor of simple interest and compound interest shall we move on so we want to solve uh the the same question in a conv i mean in a shortcut method first of all let's see how wait what's the shortcut for this all right okay listen always the reference years given they have given for double right they have given for double double is how many times two times okay so whatever the reference it could be double or it could be triple or it could be five times or it could be six times whatever the time duration given for the number of times they give you that you take it as reference in the question the reference is given for double or triple double so that is to be taken as n whatever the reference they give you right for double or triple or four times or five times the reference the first case amount they give you that you have to take it as n okay and what is n in the problem given for double how many years they have given in the question huh for double they have given four years yeah okay so that end will be for here understood now the required number of times is how many times 16 times guys always the second case amount will be the power of the given number of times okay so how do you write 16 in terms of 2 power 2 to the power 4 now please understand here the power has to be multiplied with this n what is the power of 2 4 right so 4 n will be the answer what is n we got already 4 so 4 into 4 is 60. suppose had the question been for 64 times how do you write 64 in terms of 2 power 2 power how much is 64. 2 power 8 is 64 check 2 power 6. now what is the multiplier for n now the power right what is the power 6 n so what is n already we have 4 so the answer for this is 24 years if it doubles in 4 years for it to become 64 times it is 24 years guys always don't expect for double okay sometime they give you for triple it'll take so many years for how many in how many years it will become nine times 27 times 81 times because if they give you for triple what are the powers of 3 3 power 2 which is 9 3 power 3 which is 27 3 power 4 which is 81 so if they give you for triple they'll always ask you question for nine times or 27 times or 81 times or 243 times all these are what powers of three see here if they give you double they may ask you a question for four times four times is what two power two they may ask you for eight times what is eight times 2 power 3 they may ask you for 16 times 2 power 4 all these are powers of 2 so if they give you for double always the required number of times will be power of that number only for power of 2 only if they give you for triple required number of times will be power of three only so this is for double case okay if you want you can take down for triple also if they give you for triple or triple if they give you triple is three right that is taken as n years okay so then what they'll ask the question is nine times they give you four triple they'll ask for nine times or 27 times or 81 times so 9 times means what power of 3 3 power 2 so what is the multiplier for n now the power of 3 which is 2n years understood so what about if it is 27 times 3 power what 3. so what is the multiplier for n 3n understood is it clear is it clear everyone now what if they ask if they give you 5 times they'll be asking for how many times 25 times 125 times 625 times like that it will be so here the base the reference of case one number of times will become a reference for you case one whatever case one amount that will become a reference in terms of that reference only the case two amount has to be expressed so that is the idea of shortcut you understood so what is to be multiplied with n the power of the base power of the base what is the base power here 2 right 3 power 2. so 2 has to be multiplied with n you understood have you understood everyone please tell me is that clear now tell me how do you solve this first of all guys required number of times is eight times and i mean a given number of times is eight times and the required number of times is 128. now tell me is 128 a power of 8 no if it is a see just check raise the power of 8 would you get 128 you will not get so in that sense tell me both 8 times and 128 times are a power of what common number both are powers of 2 only so please understand the previous question in the previous question in the previous question they have given for double and they have asked for 16 times so 16 is a power of 2 so double we took it as n okay because required number of times 16 is a power of 2 but in this question required number of times is how much 128 and the given number of times is 8 is 128 a power of 8 definitely not so what you do express both 8 times and 128 as a common power 2 power 3 is 8 2 power how much is 128 2 power 7 so 8 times should be expressed as 2 power 3 tell me what whatever is the power that should be the multiplier for n yes or no so 3n is equal to how many years they have given for 8 times how many years they have given 12 so what will be in 4 n will be equal to 4. now tell me for 128 times what power of 2 is 128 2 to the power 7 so what should by multiply with n 7 into n n is already we know which is 4 and the answer is 28 years you understood guys understood everyone is it clear shall i give you one more question shall i give you one more question okay listen let me write down here a certain sum of money triples in say seven years as per ci in how many years it would become 27 times this if it is as per ci question what you need to look at is given number of times is triple triple means three times and required number of times is 27 27 so you have to check what is 27 a power of 3 yes so if that is the case then given number of times itself is taken as reference three times is n what is n equal to seven years and required number of uh times is what 27 that means three power how much 3 which is what into n what into n all right what is the power of 3 here 3 right so 3 n what is 7 i mean what is n here 7 right so answer is 21 years understood so why we could not do the same thing for the previous problem why we could not take 8 as a reference because 128 is not a power of 8. so we express both 8 and 128 in terms of what two powers understood but here 27 is clearly a power of three triple so therefore triple itself is taken as n n is equal to seven years for 27 times it is 3 it can be written as 3 power 3 the power of 3 has to be multiplied with n which is 3 n n is 7 so 3 7's are 21 is the answer have you all understood is it clear is it clear everyone online students please tell me one more i'll give you many questions don't worry is it clear shall we have more questions on this shall we have more questions on this so what you have to see for type three questions on compound interest is the given number is the required number of times is the power of given number of time that you have to see if it is so the given number of times is taken as n required number of times is whatever is the power of that multiplied with n that's it shall we move on guys to solve an expression okay oh you want more questions right write down the questions i'll just give the questions okay guys it will not be there in the slide i'll be giving more examination questions later but for now if you want to practice i'll give you more questions take down but it will not be there in the slides okay please take the questions a certain sum of money becomes five times of itself in ten years as per ci in how many years it would become 125 times of itself very good answer is so what did you first of all observe what did you first of all observe the required number of times is 125 and what given number of times is phi is 125 a power of 5 guys tell me is 1 2 125 a power of 5 what power of 5 is 125 pi cube so what you should be taking from that power only 3 into n that's the answer right what is n given in this question 10 so 3 tens are 30 years is the answer is it clear everyone guys is it clear you understood you understood so what do you observe in type 3 equations of compound interest required number of times is it a power of the given number of times that you have to observe clear one more question okay should i write that step 5 times is n and that is equal to 10 125 times is 5 power 3 which is 3 into n is it required to be written not required okay let me give you one more question okay a certain sum of money becomes four times of itself four times of itself in 12 years as per 4 times of itself in 12 years as per ci in how many years in how many years it would become 32 times of itself tell me guys in this problem can we take four times as a reference why why we cannot take four times as a reference 32 is not a power off answer is check see can we take four times as a reference here no why if you raise the power of 4 you will not get 32 right 4 power 2 is 16 4 power 3 is 64. you would not get 32 as a power of 4 right so therefore what you need to do express 4 times as both 4 and 32 can be expressed in terms of what common number 2 right how do you write 4 times 2 power 2 how do you write 32 times 2 power 5. now what into n for 4 times what into end you have to write all right power right 2 into n so 2 into n is equal to how many years they have given 12 years if so what is n 6 now for 32 times it's 5 into n correct answer for this question is 30 years guys have you understood the difference between this question and this question what is the difference in the first question what i have given here the required number of times is the power of given number of times what power third power so that you have to multiply with the given number of times a given number of years 3 into 10 is the answer but here required number of times is 32 given number of times is 4 32 is not a power of 4. what do you do 4 times and 32 times are powers of 2 4 times is 2 power 2. so reference number of years is not n it will be 2 n 32 times is 2 power 5 reference number of years will be 5 into n now 2n should be equated to what for 4 times how many years it took 12 years so therefore n is equal to 6 understood understood everyone please tell me is it clear please copy this okay because it will not be there in the slide guys is there any doubt still please tell me you got the idea of this type type 3 2n is equal to 12 means what is n 12 by 2 come on 2 n is equal to 12 right to 1 0 to 6 right or 12 by 2 which is equal to 6. then substitute n in the second one which is 5 into n one more one more no we should twelve y four sir where is four why 4 n we should take 12 no no n we should take us the given number of years only if i told you right if the required number of times is a power of given number of times 125 is a power of 5 what power of 5 third power of y in that case n will be what 10 so what power of 5 is 125 third power of 5 so 3 into n will be the answer but here 32 times is not a power of 4 4 part 2 is 16 4 part 3 is 64. so why what you do 4 times x plus in terms of 2 power even 32 times express in terms of 2 power so 2 power 2 is 2 n and 2 power 5 is 5 into n so 2 n is equal to 12 years it is not n is equal to 12 2 n is equal to 12 therefore n is equal to 6 but here n is equal to 10 y because the required number of times is the power of given number of times understood one more problem shall we so hope your doubt is clear now yeah yes okay let's see how you take up this question a certain sum of money certain sum of money becomes six times of itself six times of itself in 20 years in 20 years as per as per ci in how many years in how many years it would become 36 times of itself what is that you need to first of all identify required number of times and given number of times 40 years is the answer very good first of all what is that you have to see required number of times and given number of times is it a power of given number of times 36 is what power of n what power of 6 6 square so multiplier should be the power of 6 which is 2 and what is n given 20 so in this question the given required number of times is a power of 6 therefore this itself is n what is n 2 20 is n okay so therefore it is 2 into n y because 36 times means what 6 power 2 which is 2 into n and that is 2 into 20 which is 40 years understood understood one more take a certain sum of money becomes nine times of itself in 15 years as per ci in how many years it would become 27 times guys tell me is 15 n or something else is n is 15 only is n as the previous problem or something else is n what do you see first of all why look at this required number of times 27 is it a power of given number of times definitely not right so both 9 and 27 can be expressed as 3 powers 9 times can be written as 3 squared and 27 times can be written as 3 cube so for 9 times what is the reference number of years is it n or what 2n what is that equal to for 9 times given 15 so therefore n is equal to what 7.5 years therefore 3n will be 3 into 7.5 and the answer is 22.5 years guys hope you got the fair idea on type 3 these kind of questions are never asked but never asked in the history of ca foundation or cacpt this is i am giving sometimes to be on safer side you must know this also okay only these kind of questions were asked so far but what if they asked like this you should be better prepared right you understood the difference between this type and this type what's the difference what same and what required number of times is the power of given number of times in that case what what power that should be multiplied with the given number of years that's it but here given number of times required number of times is not a power of given number 27 is not a power of 9 right what is the next power of 9 81 so both 9 and 27 have to be expressed as 3 powers 9 is 3 square that is 2 into n y 2 n because the power is 2 that is to be multiplied with n and 27 is 3 power 3 what should be multiplied with n the power which is 3 n understood so 2 2n is 15 years therefore n is equal to 15 by 2 which is 7.5 years have you understood online students please do respond is it clear answer is 22.5 yes so yeah you got the answer right yes any doubts any doubts please do let me know no doubts clear shall we move on so type 3 is clear right have you copied all this okay the next concept effective rate of interest guys this concept and one more concept coming up is based on whatever you learned so far only so no extra formula required but definitely there will be a question very frequently asked question effective rate of interest first of all let me explain the concept of effective rate of interest okay guys please listen to me first of all let's say you invested 10 000 how much 10 000 is your principle rate of interest is 10 percent per annum i'll give you two cases one is annual compounding and the second one is semi-annual okay in case of annual and the investment time duration is only one year how many years only one year tell me guys if it is annual compounding what is the interest that you get for one year ten percent on ten thousand will the principle change in one year definitely not it's an annual compounding right how much is the interest one thousand rupees and if you want to find the effective rate of interest that is effective rate of interest it is the interest that you got which is 1000 divided by the principal that you invested which is 10 000 into 100 how much is effective rate of interest for this ten percent okay but in semi-annual compounding what is the interest that you get for one year guys please concentrate here i'm going to divide one year into two halves why i'm dividing because principle is going to change at the end of first half year right now tell me for half a year would you get ten percent only five percent five percent on what your principle what is the principle 10 000. how much is the interest for the first half year 500. at the end of first half year what is the new principle 10 500 okay now tell me for the second half here what is the rate of interest ten or five five percent on what ten thousand five hundred how much by twenty five what is the total interest that you get for one year thousand twenty 25 effectively how much you're getting 1025 is a interest and principal is how much 10 000 into 100 so how much it is 10.25 what did you understand with this guys what did you understand by this look at the interests i mean to start up with what is the nominal rate i gave you 10 but effectively in case of semi-annual i mean annual compounding it is ten percent only so effective rate of interest and nominal rate of interest are one and the same for what type of compounding annual compounding but in case of semi-annual compounding effectively how much you're getting 10.25 percent nominal rate is how much 10 so what did you understand by this effective rate of interest will be more for semi-annual compounding or even quarterly compounding or monthly compounding effective rate of interest is same as normal rate of interest for what type of compounding annual compounding okay now i'll take the same 10 percent per annum only same one year only since you wanted one more explanation i'll change the principle okay guys you understood this if you if you want me to explain again i will change the principle okay what is the principle you want me to change changes 20 000 guys there's a purpose why i'm changing the principle because this proves one more important point okay what is that point we will see so please note this in effective rate of interest for the first case where we took principle as ten thousand ten percent per annum note in the sense note it in the mind that's it you need not copy this because you are not going to do it in this way so why am i explaining this you should understand what exactly is effective rate of interest so why i'm explaining all this this is not the procedure how you're gonna do effective you're gonna find effective rate of interest okay so what i'm gonna do guys i'm gonna change the principle but everything every other things will remain the same okay every other things will remain the same so let us do it for annual compounding now tell me for annual compounding what is the interest for one year will the principle change no within one year it will remain the same twenty thousand into ten percent which is two thousand what is effective rate two thousand divided by twenty thousand is a principle into hundred so how much it is ten percent now semi-annual will check when will the principle change in seminal compounding tell me every half a year right tell me guys for half a year how much is the rate of interest applicable only five percent right five percent on what twenty thousand how much do you get thousand rupees what is the new principle at the end of half year twenty one thousand now tell me what is the next half year interest thousand fifty yes now tell me what is the interest that you get for one year two thousand fifty rupees two thousand fifty rupees now what is effective rate of interest interest for one year which is 2050 divided by principal which is 20 000 into 100 how much it is 10.25 guys if you remember earlier i took p as 10 000. what was effective rate of interest for annual and what was effective rate of interest for semi-annual it they were the same right now what did you understand by this effective rate of interest doesn't depend upon what principle irrespective of principle effective rate of interest i mean principle could be anything effective rate of interest doesn't change understood effective rate of interest will is independent of principle it doesn't depend upon the principle is that clear so i just wanted to say few points on effective rate of interest what is that it is the rate of interest it is the rate of interest calculated for one year for how many years one year why do we calculate it for one year is see in the procedure also i explained what for one year only right why do we calculate effective rate of interest for uh one year is always nominal rate of interest is given for how many years per annum means what one year nominal rate of interest is for one year right ten percent parana means for one year it is 10 correct so effective rate of interest is always comparable with what nominal rate of interest if you want to compare effective rate of interest with nominal rate of interest it should be always calculated for how many years one yes why do we call it for one year tell me so that so that it can be compared with can be compared with what nominal rate of interest now guys tell me for annual compounding will there be any difference between effective rate of interest and normal rate of interest tell me for annual compounding will there be any difference between effective rate of interest and nominal rate of interest no so we can write e r i is equal to nri not a non-residential indian henri here means nominal rate of interest okay now for semi-annual for semi-annual or quarterly or monthly compoundings will it be more than nominal rate of interest or less than normal rate of interest eri lesser which one is lesser effective rate of interest is greater than nominal rate of interest yes next point e r i is independent of what principle is that clear enough does all this point make sense now all these points are justified now tell me all these points are justified now as i said eri is not calculated as the way i did earlier i just wanted to justify these points how eri is equal to nri for annual compounding how eri is gonna be more than nri for semi-annual compounding or other compoundings how eri doesn't depend upon the principle remember we took two types of two principles one is ten thousand we took for ten thousand we calculated effective rate of interest for yearly compounding effective rate of interest for half yearly compounding we got 10 and 10.25 percent remember and i changed the principal to 20 000. again 10th 10 percent and 10.25 percent did it change no that means to say what effective rate of interest doesn't depend upon the principle it is independent of principle how to calculate effective rate of interest we'll see now right guys you all know what is ci formula tell me what is ci formula p into 1 plus i whole power n minus 1 this is c i right this is c i now if you know ci formula getting effective rate of interest is very easy guys there is a p here in the ci formula now tell me effective rate of inter interest does it depend upon the principle no so what you do just exclude p from it and write the formula what is it 1 plus i whole power n minus 1 this is effective rate of interest this is what effective rate of interest so do we have to buy heart extract things here no same ci formula exclude what from it p from it so and mostly they will ask effective rate of interest as a percentage value so if you want a percentage value so percentage eri will be what you need to do tell me multiply with 100 the same formula but what do you do multiply the whole thing by 100 are these points clear on effective rate of interest so what should come to your mind when you talk about effective rate of interest effective rate of interest is always calculated for how many years one year what next effective rate of interest is always equal to nri for what type of compounding all right eri is equal to nri for what type of compounding annual compounding so eri will be more than nri for semi-annual or quarterly or monthly compounding okay now eri does it depend upon the principle no and coming to the formula of eri just remember what the formula of compound interest what do you exclude from that p because it is independent of principle so if you want to verify guys uh we took an example of what semi-annual compounding semi-annual compounding what was nominal rate given i gave you 10 percent per annum correct how many years i gave you one year because it is always calculated for one year tell me guys what is n for semi-annual compounding 2 into number of years correct for semi-annual compounding what is n 2 into number of years number of years is always taken as how much for in i mean eri 1 here because it is calculated for 1 year always why because it should be comparable with nri nri is always given in per annum for one year so eri also should be calculated for one year so why we have into one so what is n 2 tell me what is i guys 0.1 divided by 2 which is 0.05 now what you need to do plug in those values guys tell me what is 1 plus i 1.05 raise the power to what array and 2. press into press equal to the value get squared yes or no 1.05 press into press equal to the value get square what do you do after that minus 1 into what 100 how much 10.25 how much did we get earlier in a conventional method same 10.25 percent only yes you remember for semi-annual compounding we got 10.25 percent as effective rate of interest if the nominal rate of interest is 10 percent using the formula also we are getting the same what is that you need to do first of all when you are finding out eri please understand the conversion has to be correct for semi-annual what is the conversion 2 into number of years but always for number of years what do you write 1 why eri is always calculated for 1 year in place of number of years it's always 1. so 2 into 1 is 2 and i nominal rate of interest is 10 percent means 0.1 divided by what 2y for semi-annual compounding you will not get the entire rate of interest rather half of it so why dividing by 2 which is 0.05 in place of 1 plus i what do you write 1.05 and raise the power to 2 how do you raise the power to 2 press into press equal to the value get square then do what minus 1 into 100 so don't you get 10.25 percent you will get right so have you understood how to find eri have you understood everyone please tell me online students i'm waiting for your response shall we solve more problems on eri that is very important concept very often they ask questions on eri okay shall we move on shall we okay so this is the formula for eri the first formula is the fractional value formula the second one is percentage formula so how to get eri formula tell me from ci only exclude what from it p from it ah one second calculation ah okay listen okay what type of compounding is it semi-annual compounding sorry semi-annual compounding and what is nri i gave you 10 per annum and how many years they'll not specify how many years it should always be taken as one year why eri is always calculated for one year clear am i clear i'm repeatedly saying eri is always calculated for one year right now what is n for semi-annual compounding two into number of years in place of number of years i've written one by one year only into two right what is i nominal rate of interest is 0.1 divided by 2 because for half year only 50 of the interest is applicable so divided by 2 you have to do so 0.05 what is the first thing that you feed in this formula within the brackets yes that is 1 plus i i is 0.05 when you add 1 to it don't use calculator to add 1 to it it will become 1.05 yes please respond 1.05 right then raise the power to n what is n 2 press into plus equal to if you do the value get squared then what you do minus 1 in the formula is a minus 1 so minus 1 out of the bracket into 100 you have to do so the answer is 10.25 if the nominal rate is 10 per annum and if it is semi-annual compounding what is eri 10.25 you understood is that clear everyone is that clear please respond is it clear yes shall we move on to solve questions more questions right now have a look find the effective rate of interest corresponding to a nominal interest rate of 12 percent per annum compounded what monthly what is the first thing that you have to do conversion what is n for monthly compounding everyone n number of n n 12 into number of years tell me in place of number of years what i should write always eri is calculated for 1 year so n is equal to 12 what is i guys 12 means 0.12 divided by what 12 what is it 0.01 now guys tell me eri is equal to 1 plus i whole power n minus 1 since it is percentage eri whole thing multiplied by 100 tell me what do you type first 1 plus i 1.01 raise the power to what 12 press into keep pressing equal until the counter number is how much 13. then what you do minus 1 then what do you do into 100 please do the calculation and tell me what is the answer 12 point 6825 percentage have you understood everyone what is the first thing that you have to do conversion depending upon the type of compounding they give you please make the conversion then do the calculation let's do you have to remember extra formula for eri no what is that you need to remember if you know ci exclude p from it and don't forget to multiply 100 at the end because it is always a percentage value have you all understood the calculations yeah please do respond is there any difficulty in getting the answer or understanding this please do let me know everyone understood only few are responding how about others yes okay shall we have the next question then okay yeah what do you what is the first thing you need to do conversion what type of compounding quarterly tell me what is n 4 into 1 which is equal to 4. what is i 8 means what 0.08 divided by 4 and it is 0.02 what is percentage eri 1 plus i whole power n minus 1 into 100 one step calculation guys 8.24 is it 8.24 percent very good yes 8.24 so don't forget to do the calcul i mean the conversion that's the very thing first thing that you should do for not just eri problem even for compound interest problem also right there also you do the conversion rate depending upon the type of compounding what is n and what is i you'll write but here what's the difference while finding n yes type of compounding you will do into always one because number of years is always taken as one for eri we want to do one more example three find find the eri corresponding to corresponding to nri nri means nominal rate of interest of 9 per annum compounded semi-annually compounded semiannual tell me what is n and what is i n is 2 is is that the answer everyone got is that the answer 9.2025 got it understood please ask me if you have any issues with this no doubts all clear everyone okay shall we move on the next concept depreciation okay guys you know what is appreciation what is appreciation increase in the value of your money if you invest 10 000 obviously the amount that you receive will be more than what you invest so for appreciation out of a and what is appreciation a is equal to p into 1 plus i whole power n correct so tell me in appreciation which is greater a or p a is always greater than b now what is depreciation basically the value of an asset keeps reducing with time in appreciation it keep increases with time so what is appreciation appreciating asset the value of an asset whose value keeps increase keep keep increasing with time is called as appreciating asset can you tell me an example which appreciates gold gold is an appreciating asset land is an appreciating asset but how about furniture depreciating how about building depreciating asset how about vehicle machinery and all depreciating assets electronic gadgets depreciating assets so you understood so appreciating asset the value of an asset keeps increasing with time so always a is greater than b whereas depreciating what is depreciating asset the value of an asset like machinery furniture and what and all buildings etc will reduce with time such assets are said to be depreciating assets all right for depreciating asset the future value see always tell me guys amount when do you get the amount in the future or today in the future let's say your investment period is five years so obviously at the end of five years means it's a future value only right so amount is always a future value whereas principle is always present value please remember amount is always a future value whereas principle is present value all right okay for depreciating asset the furniture i mean the future value a always future value is what a will be less than the p in case of appreciation a is greater than b in case of depreciation a is less than b is it clear now let us see the formula for depreciation guys if you know appreciation formula getting the formula for depreciation is very easy so please understand a is equal to p into 1 plus i whole power n if you write it as appreciation it's going gonna be 1 minus i whole power and this is depreciation and always a is less than p for your reference for appreciation is greater than b and what is appreciation formula p into 1 plus i whole power and please understand in appreciation i mean depreciation problems where association this is appreciation and this formula is depreciation 1 minus i depreciation 1 minus i appreciation one plus i okay please understand in depreciation problems sometimes they'll give you scrap value say for example you purchase a vehicle okay you purchase a vehicle let's say the vehicle's lifetime is 10 years the lifetime of a vehicle is 10 years alright so after 10 years it will become what scrap when will it become a scrap in the future or today future only future value is always a orp so why this graph value is taken as a because it the the the depreciating asset will become a scrap when in the future so future value is always a okay then present value or a cost price so when you purchase a vehicle or a machinery and all today only right so cost price is always a present value is it clear and you need to remember one more thing guys let's say you have a vehicle today okay that was cost is one lakh today's cost is one lakh after three years if you want to sell it will the cost will be less than one lakh or more than one lakh ah you want to sell it it's a depreciating asset right today's cost is one lakh okay you bought the vehicle by paying one lakh and after three years you want to purchase a new vehicle so by selling this okay obviously you can't get one lag right obviously it's a depreciating asset you'll be getting less than what you bought for right and suppose let's say you have a vehicle today i mean it's not a new brand new vehicle whose value is estimated to be let's say 25 000. it's an old vehicle actually its value is estimated to be 25 000 today's value okay what would be its value in when three years ago three years ago will it be more than 25 000 or less than 25 000 obviously more i'm not talking about after three years three years ago definitely the value will be more since it is depreciating asset yes or no you're getting it see suppose they ask by giving you present value of the school when let's say a machinery is 25 000 always you can't take present value as p that is deceiving uh word actually okay so if they give you 25 000 as a present value and if they ask you to find what is the value of what would be the value of a vehicle three years ago or what would be the value of a machinery three years ago guys three years ago the value will be more than twenty five thousand or less than twenty five thousand more so what is this twenty five thousand lesser value is always a or p in depreciation lesser value which is lesser value and depreciation amount so even though in the question they say present value of the vehicle is 25 000 that is not to be taken as p because what is last year three years ago three years ago means its value will be more than 25 000 always the greater value in case of depreciation will be what p so you need to find out p what is given as a suppose one more example i'll give you present value is present value is 25 000. if they ask you to find the value of this after three years after three years tell me in that case after 3 years the value will be less than 25 000 more than 25 less so what will be 25 000 this time around p or a p and what will be asked here a will be asked you're getting the difference you're getting the difference three years ago or four years ago if they ask that is the value which is more than today's value so more greater value always in depreciation will be what p or a p so depending upon is it with it is it ago or after depending upon that you have to decide which is a and which one is p is that clear yes it depends upon the demand again if people don't want to buy it obviously the value will be less so antics and all it depends upon the demand will be very less it's an appreciating asset as you said so you will not be applying depreciation here for appreciation uh appreciating asset you will not be applying see in appreciation a is equal to p into 1 plus i whole power for depreciation 1 minus i whole power f right whether in the question can be asked once again whether in question can be asked in percentage and depreciation yeah they'll they'll give you rate of depreciation they'll specify you will have to convert that into decimals a fraction and one more thing can you please explain three years ago example once again sure sure listen i'll explain that example with both the cases okay the value of a scooter today is 25 000 present value of a scooter is 25 000 what would be its value after three years you know scooter is a depreciating asset so after three years will will the value be less than twenty five thousand more than twenty five thousand less than lesser value is always what in depreciation a so a you'll have to find out what is given to us is p this is one case understood after when they ask that is a present value will be p only but sometimes they'll give you present value of the scooter as 25 000 they'll ask value three years ago three years ago so since it is a depreciating i said if the value today is twenty five thousand three years ago definitely its value would be more or less more so greater value is what in depreciation p or a p so what is that we are asked to find p or a p three years ago means obviously its value will be greater greater value is always p given value is a even though they have given present value of a scooter as 25 000 that is a deceiving statement normally what you take present value as p only you would take but please understand if they ask and go present value will not be p present value will become a after years after four years after after 10 years if they ask present value will remain p only have you got have you got the point online students guys will solve questions don't worry have you understood the concept first of all yes clear let's solve the questions on depreciation okay a machine with the cost price of rupees 3 lakh depreciates at 10 percent per annum find this crap value if the life of the machine is six years scrap value means a or b scrap value when the machine in the future only it's gonna become a scrap right so future value is always a so scrap value is a what is this three lakh cost price is taken as b and what is this depreciation rate ten percent means zero point one correct yes or no and what is this six years n value correct now what is depreciation formula a is equal to b into 1 minus i whole power n guys listen here few people will have a problem subtracting a decimal from 1 1 minus 0.1 right please concentrate here you can do the calculation later on few people will have a difficulty in subtracting a fraction 0.15 from 1 if i subtract what do i get will have a problem subtracting 0.15 or 0.25 from 1. so what you do is assume 10 is 10 only okay and assume this one is what 100. it's always easy for you to subtract 25 from 100 right or 10 from 100 right what is 10 100 minus 10 90 but that is percentage 90 means what 0.9 instead of 1 minus 0.1 is basically 0.9 if you don't know suppose if you get confused what is 1 minus 0.1 suppose 1 minus 0.15 suppose you will not suppose if it is confusing you what you do take this one as hundred is the percentage only see suppose i is given as 10 here it is given as 10 percent so one is considered as what 100 100 minus 10 is 90 10 10 100 minus 10 is 90 but still we have not converted that into fraction 90 means 0.9 so you type what 0.9 in the calculator don't use calculator for doing 1 minus i guys you understood this you understood this what i said if you are having a difficulty subtracting a decimal from 1 then always take the decimal as in terms of percentage but one you consider as 100 but later on after doing 100 minus 10 90 that you have to convert into fraction 90 means 0.9 right is there any difficulty guys two digit number after a point there is no zero so it's point nine so what do you do guys type zero point nine type zero point nine what do you do after that raise the power to how many years six a is equal to p into 1 minus i whole power n so what do you type in place of 1 minus i 0.9 raise the power to n n is how much 6 that means the counter number should be 7 into what p what is p 3 lakh so what is the scrap value or amount 1 lakh 59 000 59 000 for 32.3 you understood yes and and i i want you to observe one very important thing in your calculator guys tell me what is one minus i value is it less than 1 or more than 1 1 minus 1 plus i is always more than 1 right 1 minus i is always less than 1 okay tell me a value which is less than 1 0.8 or zero point and whatever value all right within this zero to one zero point five okay you type zero point five in the calculator and keep raising the powers keep raising the power what do you observe as you increase the powers of 0.5 what is going to happen what is happening actually the values increasing or decreasing my question is by by increasing the power of the value which is less than one the value which we picked as less than one is 0.5 and we kept on raising the power what did you observe the value reduces yes keep that in mind always the value reduces if you increase the power suppose if the value is more than one type 1.1 in the calculator and increase the power what do you see effective value will keep increasing yes or no please keep it in mind this will help you out to solve some of the questions for depreciation problems let's say for example you get some value over here right 1 minus i value you get right so suppose the 1 minus i value is lesser than the required if you want to increase the power has to has to reduce or increase say let's say a minus a divided by p what is a divided by p for this example a is 1 lakh 59432 0.3 divided by p is 3 lakh and that is equal to 1 minus i whole power n correct what is a by byp in this question for this example tell me the value 0.53 one okay fine and let's say 0.9 is 1 minus i but you don't know what is n value sometime by giving a p and i they may ask you to find in how many years it becomes a scrap okay by giving a p and they may ask in how many years it will become a scrap so options are five six uh wait wait let me say six seven then eight option d none guys always make it a usual practice that you would plug in what option moderate or what least option a is six sorry option a is six option b is seven option c is eight and option d is none what do you do type 0.9 in the calculator keep raising the power up to what seven first seven means what counter number should be eight that means counter number should be eight so what is the value is it more or less less less so the power has the value has to increase if the value has to increase the power has to decrease so the only power which is less than seven is six so you can take six as young but actually you need not do by raising the power you get 0.531 right by raising the power you get 0.531 for what counter number 7 actual power is six understood guys is it clear but here they have not asked you to find and if they ask you to find and you have to be very careful especially with depreciation problems because the effective value one minus i is less than one if you increase the power the value reduces if you decrease the power the value increases keep that in mind always solve the next question guys how many years option c six years yes it's similar to what i discussed just now okay can you tell me what is a and what is p in this question a is equal to 3 forty five point seven two eight and what is p in this question twelve thousand how do you decide that a is this and p is this a is always less than p so a is equal to p into one minus i whole power n what do you do first of all divide a by p what is a by p what is a by p 2 6 okay only four digits you write enough now what is one minus i guys one is taken as hundred i is twenty so hundred minus twenty is eighty percentage what is eighty percentage zero point eight power n what do you do type 0.8 in the calculator press into keep pressing equal until you get this value what is the counter number 7 if the counter number is 7 what is n 1 less than that which is 6 and the answer for this question is option c have you understood guys online students please do respond i didn't understand how to take p and a fine how do you know it's a depreciation problem they clearly say that a machine depreciates at 20 percent the moment you say depreciating rate it is depreciation problem all right they've given the cost and the scrap value realized at the time of sale being twelve thousand and three thousand one forty five point seven two eight they've given the cost price and they give they have given the scrap value so cos scrap value when when will the machine become a scrap in the future what is future value a or b scrap value is always a in the future only the the the asset will become a scrap so which is a actually the lesser value is a and the greater value is b is it clear amongst this graph value and so obviously scrap value will be less right than the cost price so lesser value is a and the cost price the higher value is b is it clear now is that point clear is that point clear ruksha yes now let's see the calculation part okay now what do we know we know a we know b and we know what i twenty percent i said when you whenever you're subtracting a fraction from 1 always do what take that 100 100 minus 20 is 80 80 percent is written as 0.8 so the value of 1 minus i is 0.8 whole power m where did where did this p go to the denominator of lhs so a divided by p let me write that okay a divided by p what is a divided by p a is 3145.728 divided by p is 12 000 don't you get 0.2621 please tell me 0.2621 and that is equal to the value of 1 minus i is 0.8 whole power n all right now what is that we need to calculate the value of n so how do you do that type 0.8 in the calculator press into keep raising the power until you get 0.2621 approximately for that tell me for what counter number here you got 0.2621 by raising the power what is the counter number i think i guess it is 7 right it is 7 isn't it ok if the counter number is seven what is the actual power one less than that which is six so therefore n is equal to six understood understood is it clear now one last concept with si and ci the problems will be asked based on si and a ci so how to go about it okay yes so how will they ask questions combining si and cis they'll say uh two year difference or two compounding the difference between s i and c i for two compoundings or two years okay two year difference or two compounding difference difference between c i and s i for two compoundings or difference between c i and s i for two years okay both one and the same only okay so we will take a question i'll give you all methods okay there are three methods which i'm going to explain to solve this question okay the three methods that i'm giving is first is a conventional method second one is verification method and the last one is a shortcut okay please concentrate here guys what is the question this question says difference between si and ci for how many years two years is how much 25.2 what is the rate of interest six percent per annum find what some some means what principle some means what principle now difference between c i and s i means which is greater c i or si uh-huh ci is always greater right so can i write the difference as c i minus s i and that is equal to how much they are given 25.2 rupees the difference between ci and sr is 25.2 rupees let's tell me in both the cases what is same principle is same principle is same so can i take out the principle from ci as well as si so if i take out principle from ci what will be remaining minus 1 plus i whole power n minus 1 you remember the formula for ci 1 plus i whole power n minus 1 so this is what is remaining if i take out p from the ci minus tell me from si if you take out p what is remaining pr percentage tr percentage or tr by 100 yeah and that is equal to what 25.2 you see you can do this in one step in the calculator how one plus i is what guys what is i here 0.06 correct what type of compounding it's annual compounding if not specified so what do you type in the calculator first within the bracket 1.06 raise the power to what 2 raise the power to 2. how did you raise the power to 2 press into press equal to the power gets i mean the value gets squared would you write that value would you write that value on paper not required what do you do instead m plus y m plus it's a positive value then what you type one type one press what this time okay look at the sign and tell me m minus next what you do t into r guys time how many years two years into r is how much person six press what percentage six percentage then press what m minus on m plus m minus then mrc what's the result of that zero point zero zero three that's it or you have more digits after that 36 and that is equal to 25.2 tell me what is p 25.2 divided by 0.0036 and the answer is seven thousand have you understood this conventional method everyone yes please tell me have you understood this or should i explain again online students explain fine listen guys what is given in the question the difference between ci and si for how many is two years okay on a certain sum how much sum they have not given some means what principle is how much 25.2 rupees so difference between ci and sr means which one is greater ci so can i write difference as c i minus s i is equal to how much they have given 25.2 rupees is this first step clear first of all tell me clear now tell me from ci formula and uh si formula what is common p if i take out p what will be remaining from c i 1 plus i whole power n minus 1 this is what is remaining from ci formula there is a minus here so i'll write minus what is si ptr percentage already p has been taken out what will be remaining within tr percentage yes that closes the brackets right now which is equal to how much 25.2 guys the only unknown here is p so you solve this expression in one step in the calculator how do you do it type 1 plus i first what is 1 plus i i is 0.06 so 1 plus i will be 1.06 raise the power to what what is n two years press into press equal to for raising now how do you store that value guys press m plus understood then type 1 how do you store that value look at the sign and tell me m minus then t into r t is how many years here 2 into what is our 6 press what percentage how do you store this m minus how do you recall everything from the memory mrc right tell me what is the value you got in the calculator 0.00 is equal to how much 25.2 therefore p is equal to 25.2 by 0.0036 how much it is is it seven thousand everyone have you got the answer now seven thousand everyone please tell me is it seven thousand yes this is the conventional method okay guys even though it's a conventional method how much time it will take does it take one minute huh will it take two minutes come on what your what are you writing basically ci minus si is equal to 25 point the difference you will write down then you will carry out the calculation within the in the calculator itself and you will write this step then you will divide whatever value of return divided by that value that's it so it will take maximum 40 to 50 seconds not more than that you will have 1.2 minutes that means 72 seconds you can still be able to solve in conventional method but i'll give you shortcut so that you can solve it in five seconds right now let us see the verification method guys you may be thinking why do we verify why do we verify why verification method is required verification method is required to solve some of the problems which we see later but still verification method you learn first for some kind of problems a verification method is very very important without verification method you cannot solve the questions there are some questions actually on ci and si where verification method is the must and it will give the answer quickly okay now what is basically verification method guys here we ended up getting the principle so here what we do we start with this principle and we should get what the difference as 25.2 if we get so it is successfully verified correct how do you verify your answer you take as the data and you end up getting the question that is the verification method right so what is the rate of interest i gave you six percent per annum how many years two years guys please concentrate this is very important as i said so draw the line and divide the line into number of parts equal to number of years how many years here two years so this is one this is two is it clear the first step please understand for verification method on top of every year you will be writing si on top of every year you will be writing si at the bottom of every year you will be writing difference between c i and s i at the bottom of every year you will be writing difference between c i and s r now guys for s i will the principle change for s i will the principle change for s i no so tell me what is si for of si for seven thousand at six percent per annum one year seven thousand into six percent for twenty rupees this is si for first year will si be different for second year no because principle will remain the same for s i so s i will be same for 20 rupees only understood the first step on the top of your every year what do you write si now at the bottom of every year guys tell me will the principle change within one year for annual compounding will it change no if the principle doesn't change will there be any difference between c i and s i whatever is s i the same will be c i s or no because the principle is not going to change within one year whatever the interest that you simple enter that you get for one year the same will be the simple compound interest you get for one year if both are equal what will be the difference for first year both are equal if you take the difference 420 minus 420 is zero always the first year difference will be zero why principle doesn't change within one year right correct so difference will be zero for the first year now how to get the difference for the second year guys this is very important point please concentrate you're writing the difference of the second year right to the left of second year whatever numbers you've got put a box like this add the numbers 420 plus 0 is 420 write down that 420 the sum of these numbers into whatever the rate of interest what is the rate of interest given 6 percent what is 4 20 to 6 percent 25.2 so what is that we are supposed to get actually the total difference for two years should be equal to how much 25.2 guys first year difference is almost zero second year difference is 25.2 so total difference is how much 25.2 we started with 7000 as a principle we ended up getting the total difference as 25.2 have you understood this verification method draw the line divide the line into number of parts equal to the number of years on the top of every year what do you write aside seven thousand into six percent for twenty the same will be the s i for the second year on the bottom of every year you will write the difference what is the difference for the between simple interest and component for the first year always zero because the principle doesn't change so it will be zero therefore the difference for this second year will be how do you get the difference in the second year to the left of second year put a box like this and add the numbers within it how much do you get 420 plus 0 is 420 into what the rate of interest given 6 percent so what is it 25.2 and the total difference for two years we got is 25.2 so that means whatever principle you got is correct have you all understood this verification method have you all understood here okay now at last most awaited shock tracking this is for what two compoundings only difference given for two compoundings or difference given for two years please understand what is that we need to calculate p right so p is equal to difference between c i and s i for two compoundings divided by i squared now tell me what is the difference given for two compoundings in the question 25.2 right type 25.2 what is i value 0.06 come on i decimals 0.06 how do you divide it again press equal to how many times 2 times why because denominator i square is there guys have you understood 25.2 you will type pressure divided by i value is how much 0.06 what do you do press equal to how many times 2 times why because denominator will be i square here what is the answer you're getting seven thousand how many seconds five seconds but remember this is only for two compoundings this is only for two compoundings for three compoundings for three years i'll talk about it later in the next class have you understood let's please go through these concepts today and come for tomorrow session i think i have not done much today right only four types three types then along with that eri and uh depreciation i think era and depreciation is not a big problem for you why eri if you know ci formula just exclude p from it the procedure is almost the same and depreciation if you know appreciation formula depreciation is almost the same only difference is what 1 plus i becomes 1 minus i that's it so only thing is that those three types and this last one so there's one more concept in the last one i mean there could be even three year difference but using conventional method you can even get the answer for three year difference and four year difference and all yes can you all come prepared for tomorrow's session explain the shortcut again okay the shortcut is what we need to find principle what is given to your difference or difference between c and s i for two compoundings that divided by what i square what is the difference between c i and s i for two compounds given 25.2 divided by i square that means 0.06 the whole square correct what you need to do is type 25.2 in the calculator press divided by what 0.06 since it is whole square press equal to how many times 2 times 25.2 divided by 0.06 since it is whole square press equal to how many times 2 times don't you get 7000 yes so please come prepared read everything and come because tomorrow we may start with previous paper questions yes thank you good night [Music] okay yeah so last class we were doing compound interest in that we were doing the questions on what difference between ci and si for two compoundings or two years right two compoundings if they give you difference between two compoundings or two years what is the shortcut i told you first of all conventional method we'll talk about for a while what is the conventional method write down c i minus s i is equal to whatever the difference they give you then what you do what is common between c i and s i p to take out p and write down what is remaining from c i formula 1 plus i whole power n minus 1 minus what is remaining from s i t r percentage right and that is equal to whatever the difference they give you then you have to solve this in what one step using what m plus a minus mrc now what is the first thing that you would type 1 plus i value 1 plus i means if i is equal to 3 percent what is the decimal value of 3 percent 0.03 would you use calculated to add 1 to it no so where will one get added to the left of the decimal it will become 1.03 so what you should be typing straight away 1.03 raise the power to n let's say n is equal to 5 okay so raise the power to 5 then do what m plus see for raising the power to 5 what should be the counter number six the counter number should be six just tell her no okay then type word one then press what m minus because it's a negative value then t into r press a percentage then m minus mrc you get some result right this result will go where to the right hand side and it gets divided so difference will be given divide that value whatever you get so that is the principle so that is the conventional method guys why am i stressing on conventional method is i'll give you shortcut for two year difference or two compoundings i'll give you even shortcut for three year difference but i can give you shortcut for even four year difference but remembering the shortcut formula becomes complicated thing so anyway you can solve it in 40 to 50 seconds if you do it in conventional method also by doing this you can solve it in what 40 to 50 seconds easily so you can apply the shortcut for two year difference and even three year difference don't go for four year difference if they give the ask the question for four year difference do it in the conventional method okay and i told you the verification method also and i told you clearly verification method is very very important for solving some of the problems what sort of problems we'll discuss later so how to verify guys so suppose if you get the principle what was the answer for principle for the previous question which we got 7 000 what was the rate of interest six percent how many years two years the previous problem which i am talking about right so how to verify i said draw the line divide the line into two parts why two parts because two years one year and two here right on the top of every year what you will be writing s i s i all right now s i for one year what is the principle seven thousand into six press what percentage so what is si for one year 420 rupees so will the si changes for the second year no it will remain the same because principle doesn't change for s i is it clear on top of every year you'll be writing what only s i on the bottom of every year you will be writing what difference between c i and s i difference between c i and s i now tell me will there be any difference between c i and s i for the first year so if the principle doesn't change obviously whatever is ci and the same will be the s i also both are equal values for the first year if they are equal values obviously the difference will be how much zero the first year difference is always zero how do you get the difference for the second year to the left of second year whatever you have put a box like this add the numbers within 400 420 plus 0 is 25.2 yeah 420 will be the number into what percentage six percentage so it is 25.2 and if you add the total difference first year difference is zero second year difference is 25.2 the total difference for two years is 25.2 the question was what they are given the question as the difference for two years is 25.2 find the principle so we got the principle as 7000 and we verified what with the 7000 we ended up getting the difference as 25.2 that means our principle is perfectly all right correct understood understood guys i wanted to tell you one more important thing in this verification method okay if you add every number at the bottom and at the at the bottom top and the bottom whatever you see if you add all these numbers you get the total ci that is total s i plus total difference let's tell me what is total s i 420 plus 420 is 840 plus total differences 0 plus 25.2 so it's gonna be 865.2 this is what total ci for two years how much total ci for two years what is total si for two years eight forty if you take the difference how much you should be getting 25.2 is it clear so we discussed uh till this point and i gave you the shortcut also only for two compoundings or two years what is the shortcut to find the principle for two compoundings difference between ci and si for two compoundings divided by i square now how to do the calculation what's the difference we got 25.2 i value is 6 percent that means 0.06 the whole square how do you do the calculation type 25.2 press the divided by button type 0.06 only once right how do you divide it twice by pressing equal to twice type 25.2 pressure divide by button type 0.06 since it is the whole square that means to say you need to divide it by divide it two times so how do you how do you get that by pressing equal to twice after this number so what is the answer you would get 7 000 so if you get a question on uh si difference between ci and si for two years straight away you can use this shortcut what do you do feed the two year difference or two compounding difference divided by i value i value remember it should be a decimal value or a fractional value and you have to depress how many times equal to two times so you will get the answer in the calculator itself you need not write anything on the paper am i clear everyone online students guys are these things clear so far 25.2 is a difference first it's not see if you take the difference for second year it is 25.2 yes 25.2 is also the difference for two years also right what is the total difference for two years first year difference is zero second year difference is twenty five point two if you sum them up twenty five point two only the second year difference is same as the two year difference both are one reason why because first year difference is zero whatever the difference that you get for second year the same is the difference for two years is that point clear everyone everyone is clear so shall we solve more questions on this shall we solve more questions on this ready we'll be applying only the shortcut method all right if possible the verification method also will do guys look at the question the difference between si and ci for two years on a certain sum is 64.8 at nine percent per annum find the sum so what is it difference is how much 64.8 divided by i square that is what is i value 0.09 the whole square how do you do this in the calculator 64.8 divided by 0.09 equal to how many times two times so the answer is eight thousand have you all got the answer have you all got the answer guys shall we verify this shall we verify this what is the verification technique guys draw the line divide the line into two parts on the top of every year what do you write s i s i tell me what is the s i for the first year eight thousand is the principal nine percent is the rate of interest what is it seven twenty what is si for the second year seven twenty now what is the difference for the first year zero what is the difference for the second year 720 into nine percent right 720 into what nine percent because even if you put a box like this you get 720 only right into what percent nine percent how much is the difference for second year 64.8 guys haven't we got the difference 64.8 by taking the principle isn't it that means verified verification technique is very much important for solving some of the problems what type of problem we are going to see after some time understood everyone guys is that clear the shortcut clear online students yeah tell me the answer for the second one then p is equal to difference for 2 years is how much 172.8 divided by 0.12 the whole square what is the answer 12 000. shall we verify this how do you do it s.i for the first year what is it twelve thousand into twelve percent thousand four forty and thousand four forty is the second year i also what is the difference for the first year zero what is the difference for the second year one for one four four zero into how much percent twelve percent so one seventy two point eight guys have you all understood have you all understood everyone could you explain the calculation which calculation dikshita the shortcut or the verification please be specific shortcut or the verification 8000 did not come it will come now check uh it is the difference first which is 64.8 please type it press the divide by button please follow the instructions press the divi because you need to divide and what is the value 0.09 have you pressed zero type 0.09 all right then equal to how many times you have to press tell me two times are you not getting it are you not getting it respond two year difference and three year difference please don't do it in a conventional method because i'm giving you the shortcut fourier difference also i can give you but to remember the shortcut because lot of decimal numbers you have to remember for that it will take i mean so it's a risky one please don't do that for four year difference you can take the conventional method okay yeah so verification should i explain again please tell me have you understood the verification everyone yes okay listen listen listen see guys when i am explaining please listen here concentrate here when you when the concentration shifts somewhere else obviously these things will happen please focus when i'm explaining something all right okay so so how many years they have said two years so draw the line and split the line into two parts one year and two years now on the top of every year what do you write s i what do you write s i on the bottom of every year you will write what difference and difference all right now what is si for the first year 12 000 is the principle into 12 what is twelve thousand into twelve percent fourteen forty fourteen forty is s i for the first year the same would be the s i for the second year also correct monisha is it clear yeah then the difference for the first year irrespective of whatever maybe the principle whatever may be the rate of interest the difference is always zero why because within one year the principle is not going to change whatever is the s i the same would be the ci also so difference will be zero to get the difference for the second year to the left of second year whatever numbers you've got that is one four four zero right plus zero it's one four four zero only on that how much percent you have to take whatever the rate of interest 12 so how much is it 172.8 so that is the difference for the second year and the same would be the total difference for two years because the first year difference is anyway zero right yeah so the total difference for two years is 178.2 170 2.8 and that is successfully verified and you need not do verification i said for some problems you need verification method for what type of problems i'll explain later is it clear so far don't do verification method for such problems all right yeah you're welcome shall we move on shall we move on so got the point in two year difference what to do put the put the difference in the calculator right i mean type the difference in the calculator divide by what i value i value in decimal or percentage decimal only then plus equal to how many times why twice because square is there in the denominator you have to divide it twice is it clear that's a shortcut for two year difference now let's move on to for three year difference okay suppose if they give you difference between ci and si for three years what to do first of all like i'll explain conventional method verification then the shortcut because conventional method is not required for three years and two years it is required for four years so you must do conventional method also okay now look at the question the difference between si and ci for three years on a certain sum is 38.125 guys you can't apply that shortcut which i explained for two years that is only applicable for two year difference or two compoundings am i clear am i clear okay now what is the difference they have given 38.125 at what rate of interest five percent per annum find the sum some means what principle guys what is com ci minus si they have given in the question 38.125 all right so we are doing what first conventional method right so guys tell me what is common from c i and s i principle i would take that out what remains from c i 1 plus i whole power n minus 1 minus what remains from s i t into our percentage all right and that is equal to 38.125 guys you should be able to do this in one step in the calculator what is i means five percent means 0.05 what is the first thing you have to type in the calculator whatever within the brackets so what is it 1.05 what is n here 3 what do you do after that to store it m plus y it's a positive value then type what one then type what one look at the sign it's a negative value what do you press m minus then t into r what is t guys three years into what is our phi press what percentage press what this time m minus or m plus negative value so m minus m rc what is the result of that 0 7 six to five is that the value zero zero zero point zero zero seven six two five and that is equal to thirty eight point one two five just divide and tell me what is p thirty eight point one two five divided by zero point zero zero seven six two five how much five thousand 5000 is the principle right online students no one responded have you all got 5000 as the principal is it 5000 or should i explain the calculation again yes listen yeah those are still struggling please listen what is the first thing that you will do c i minus s i the difference they have given so see difference between what c i and s i what is that 38.125 okay what is common between ci and si principle so we will take p outside what is c i formula p into 1 plus i whole power n minus 1 if i take out p what is remaining 1 plus i whole power n minus 1 that is from c i there is a minus sign so minus what is si ptr percent p we have taken out so tr percent is remaining all right and that is equal to 38.125 all right now you have to do the calculation in one step what is the first thing that you type 1 plus i i is 5 means decimal value is 0.05 so what do you type first of all 1.05 as a result of 1 plus i please even when i say values please type it okay 1.05 then power n what is n here 3 raise the power to 3 how do you raise the power to 3 press into keep pressing equal until the counter number is 4 then you need to store the value how do you store it look at the sign of this number it's a positive one right so you would press m plus then type 1 press what it's a negative value because -1 is there so m minus then what t into r what is t here three years into r is five press what percentage press what this time m minus then mrc store it then recall it okay now what are you getting guy 3 what is the value you got now 0.007625 all right and that is equal to 38.1 now what you need to do retain p 38.125 has to be divided by 0.007625 so what is the value 5000 is that clear is that clear everyone right three is that clear yes okay now shall we do the verification method guys okay so how do we start verification tell me how do you how do we start verification we will start with the principle which is 5000 what is the rate of interest 5 and what is the number of years three years what do you do draw the line divide the line into how many parts three parts one two three on the top of every year what do you write s i on the bottom of every year you'll write what difference irrespective of whatever principle whatever the rate of interest the first year difference is always zero what is s i for the first year five thousand into five percent which is 250. second year also sr doesn't change no 250 for the third year as well now guys tell me to get the difference for the second year what is that you're gonna do to the left of second year whatever you have add the numbers and take what percent five percent what is 215 to 5 percent 12.5 are we done no we still have one more year to go what is it difference for the third year guys tell me to find the difference for the second year what did we do to the left of second year whatever numbers we had we added then we took the rate of interest given now to find a difference for the third year to find the difference with third year to the left of third year whatever we have we need to add everything that means 250 plus 250 plus 12.5 plus 0 how much it is 512.5 on that how much percent pi percent how much is that 25.625 guys if you add all the differences don't you get 38.125 tell me 25.625 plus 12.5 is how much 38.125 so successfully verified that the total difference is 38.125 have you all understood have you all understood guys respond is this verification method clear everyone is this clear we are not clear online students guys respond no response only is it clear not clear here shall we move on shall we see the shortcut yep okay this is for what three year difference to find what principle guys difference between c i and s i for how many years three years divided by i square here also i square will be there along with that 3 plus i in the denominator extra term is what 3 plus i all right now guys tell me the calculation what is difference 38.125 i is how much 0.05 the whole square what will be 3 plus i hey guys i is 0.05 what will be 3 3.05 guys you need not write it on the paper it's only for your understanding and writing what do you first of all type tell me difference for three years what is it 38.125 type it divided by what 0.05 press what equal to how many times why because i square it us then tell me guys would you multiply 3.05 or divide 3.05 divide 3.05 because 3.05 is in the denominator answer is 5000 so by doing this you can get the answer quickly so what is the extra term to be divided in for 3 year difference 3 plus i for 2 year difference you just divide i square right here extra term that you have to divide is 3 plus i just remember that 2 year difference just divide i square real difference along with i square divide 3 plus i also so there's a decimal 6.4 something so remembering that will be a difficult task so i do what conventional measure it will take only 40 already yes epic 30 to 40 seconds now you can do it so because lot of shortcuts is too bad actually sugar should be only this much right sometimes too much of sugar you will get sugar no diabetes right sugar only should be so much it can't be right have you understood guys is it clear online students again and again i need to ask you guys is it clear clear clear huh please do respond shall we move on to solve more questions on three differences guys tell me for three year difference extra thing that you need to divide is what 3 plus i but don't forget to divide i square before that first you have to divide i square as you do in case of 2 your difference along with that again divide 3 plus i if i is 0.03 what is 3 plus i 3.03 as simple as that clear everyone yeah we'll solve some questions here the difference between si and cr for three years on a certain sum is 550.8 you have to observe what difference for how many years three years right so keep it in mind what do you type first of all 550.8 divided by what i value 0.06 how many times you have to divide two times that is i square that means what 550.8 write down 550.8 divided by 0.06 the whole square again 3.06 right what is the answer 50 000. have you all understood have you all understood guys is it clear have you ever got 50 000 as the answer have you all got 50 000 you got 50 000 you have 50 000 give it to me um ah before that we'll verify this no please don't do in the exam this will work all the time okay don't uh don't verify verification method is required to solve some question i'll tell you what sort of questions later immediately after this slide okay first we will do what verification yes for verification what you need to do divide the line into how many parts three parts on the top of every year what is that s i fifty thousand into how much percent six percent so tell me what is it three thousand si for the second year three thousand s for the third year three thousand difference for the first oh sorry i'll add one more zero no okay right difference for the first year difference for the second year to the left of second year you have three thousand into what percent six percent how much is the difference 180. difference in the third year add everything six thousand one eighty into how much percent six percent so how much three seventy point eight at all the differences now don't you get five fifty point eight you will get understood everyone understood verification method yes tell me if there is no i'm not concerned with s's concerned with nose not this nose understood clear shall we move on uh next problem you got the answer already okay you're insulting the problems here okay what is p difference for three years divided by what i square into what 3 plus i yes how much is the answer 15 000 some other answers guys tell me have you got different answers huh god it or not god i do god 15 000 sir then tell me nah if you got i'll be happy at least make me happy yeah okay what next verification will verify quickly okay so what you could do guys should i write s i s i s i difference different difference not required no what do you write first si for the first year fifteen thousand into eight percent how much twelve hundred again twelve hundred again twelve hundred difference for the first year zero for the second year twelve hundred into how much percent eight percent how much ninety difference for the third year 2496 right thousand two hundred plus thousand two hundred plus ninety six two thousand four ninety six into eight percent how much six huh six eight now add all the differences don't you get 295.66 you get right okay everyone understood clear all clear okay shall we move on yeah now comes the verification method where to use verification method all right okay problems using verification method guys only you will know what is verification method don't tell other students that a use verification method they'll not know right you know what is verification where do you do verification method right okay look at the question what sort of questions have to be solved using verification technique okay look at the question the si on a certain sum for two years is thousand two hundred at six percent per annum okay find the ci for the same time for the same duration what is given to us s i for 2 years is given what they're asking ci guys if you want to find ci you need principal rate of interest and i without principle can you find you can't so mind block mind block right so verification method plays a very important role for this kind of problems what kind of problems they'll give you si for two years they'll ask you to find ci for the same time and same duration they'll give you si for three years they'll ask you to find ci for the same time and same duration for that kind of problems you need verification technique guys what is verification technique how many years they have given two years all right all right draw what line dividing the line into how many parts dividing the line into how many parts two parts yes okay let me draw the line but tell me guys on the top of every year what i should be writing s i uh thousand two hundred for two years guys so what is s i for one year one year is thousand two hundred by two because thousand two hundred is for two years they have given so obviously s i for one year is six hundred so what i should be writing here six hundred and six hundred at the bottom of the every year what do you write difference for the second year difference what is that 600 into what percent six percent which is 36 guys i already told you if you if you if you uh get this you can easily find out ci total ci for total ci what you need to do add all the numbers total s i and total difference what is total crs what is total ci one two three six any formula we used nothing so when to use this verification method tell me when they give you si for two years when they ask you to find cr yeah have you all understood online students yes any doubts you are supposed to find ci not difference two thousand six forty it did not add total cisi to it guys once again look at the question three year s i they have given what is s i for one year s i for one year is two 2 400 divided by how much 3 which is 800 now guys divide the line into how many parts three parts on the top of every year s i for one year is 800 800 and 800 tell me the difference for the first year zero for the second year what is it eight hundred into how much percent ten percent which is eighty for the third year how much eight hundred plus eight hundred plus eighty thousand six 0680 into how much percent 10 percent so 168 correct so what is the total ci add all the numbers 1 800 plus 800 plus 800 plus 168 plus 80 how much it is two thousand six forty eight yeah finally i got some doubt what is it sir at last could you explain how to calculate one minus i whole power n like these numbers in calculator like what numbers at last okay there is no problem with this na there's no problem with this don't worry immediately after this immediately after this i'll be solving uh ica material questions so you'll get to know all the questions you'll get to see all the questions okay right guys we are successfully done with compound interest right yeah so let's move on to the ica material questions okay my material questions are done so we'll move on to ica material questions let's look at the question p is equal to thousand r is equal to five percent per annum n is equal to four what is the amount and see i it's a ladder question amount and ci they have asked what do you want to find out first of all cir amount which one is easy for you amount of ci is easier because you need not do minus one what is amount p into one plus i whole power n correct just find out amount why am i saying find out amount first if you find amount just subtract principle you get c i right isn't it guys what is the first thing you need to type in place of one plus i 22.5 12 15.50 and what is ci amount minus amount minus principle so what is amount you got one two one five point five and cr is a minus b which is 215.50 guys any doubt regarding this calculation tell me any doubt with this calculation no dikshitar should i explain this calculation in the calculator please do let me know should i explain this calculation hmm could i do that okay fine 100 will become dash after 20 years at five percent per annum compound interest off 100 will become dash means 100 means what principle it will become what that means obviously we need to find what a amount what is that connect amount and principle appreciation formula so what is it p into 1 plus i hold parent tell me the value of 1 plus i 1.05 raise the power to 20 guys you know how to raise the power to 20 press into keep pressing equal up to counter number is 21. do it fast nothing will happen to your calculators 265 so none of this is the answer clear because it is after 20 years is that the calculation correct principle is in 200 you did oh they've asked compound interest right so subtract principle no come on the question is actually uh there's a mistake in the formation of the question actually so if they ask you to find compound interest a minus p you have to do a how much it is so there are two questions here one is a another one is ci so what is ci a minus b 265 point three three minus 100 is 165.33 amount is 265.33 right clear okay the effective rate of interest corresponding to a nominal rate of three percent per annum guys what is the first thing that you need to do for era what type of compounding half early for half yearly what is n n is equal to 2 into number of years number of years is taken as always 1 so n is equal to 2 what is i 3 means 0.03 divided by what halfway compounding entire rate of interest is not applicable only half of it that means 0.015 so we got the conversions right now what is eri same like ci but p is excluded so what is it e r i is equal to 1 plus i whole power n minus 1 whole multiplied with 100 because we want percentage eri guys what is 1 plus i 1.015 because i is 0.015 when you add 1 to it don't use calculator to add 1 to it it will become 1.015 raise the power to how much 2. how do you raise the power to two into equal to then do minus one then into hundred how much three point zero double to five is the answer understood guys everyone have you all understood clear yes any doubt please do ask okay let's move on to the next question the ci on rupees four thousand what is four thousand principle six months is the time what type of compounding quarterly guys what is the first thing you have to do conversion for quarterly compounding tell me what is n four into number of years that six months means how many years point five years six months means half a year right zero point five years so what is it two right what is i twelve percent means zero point one two but quarterly compounding it is divided by 4 so how much is this 0.03 guys is this conversions clear are these conversions clear everyone online students okay now what is it we need to find the ci what is ci guys p into 1 plus i whole power n minus 1 please do the calculation 1 plus i is 1 1.03 raise the power to 2 minus 1 into p [Music] two forty three point six have you all got the answers please do let me know have you all got the answers to forty 43.6 guys yes or no shall we move on okay how many questions we solved four questions look at the next question a machine depreciated at the rate of 20 per annum on reducing balance the original cost of the machine was 1 lakh and its ultimate scrap value was 30 000 so what are 1 lakh and 30 000 means one lakh is present value that is p scrap value that is a in depreciation a is lesser p is greater right now what is it we need to find effective life of the machine effective life of the machine that means n you need to calculate what is depreciation formula p into 1 minus i whole power n guys i told you especially for depreciation for problem i you take it as 20 only and one you have considered as well 100 one you have to take it as 100 100 minus 20 is 80 but still it is in percentage what is 80 in fractional value 0.8 so what is a 30 000 what is p 1 lakh where will p go denominator of lhs so what is the result of a by p 0.3 correct 30 000 by 1 lakh is zero point three and that is equal to what remains on the right side zero point eight whole power what pull forward in now guys there is a litigation here what is the litigation let me verify that let me tell you that 4.5 years you can raise the power yes i told you yesterday if it is 4.5 years split it as power 4 into power 1 by 2 power one by two means square root and five point four years you can't find out five point five years you can find out nearest value will be only five point four now tell me guys in the amongst the given options what is the moderate one moderate one is five years so what do you do plug in five type zero point eight raise the power to five zero point zero point three two seven six but what you should be getting 0.3 the value has to decrease if the value has to decrease the power has to increase or reduce look at the value at the base i told you if the value at the base is less than one if you increase the power then only the value will reduce if you want you can check type 0.8 keep pressing into equal to value will only decrease right guys by plugging in n is equal to 5 you get 0.8 power 5 is 0.32 but what you must be getting 0.3 that means the value has to decrease if the value has to decrease the power has to increase a little bit but 0.32 is very close to 0.3 power has to increase a little bit tell me what is the only power which is more than 5 so that will be the answer because for phi you get 0.32 right for phi you get 0.32 it has to reduce a bit that means power has to increase guys i told you yesterday yesterday because of this reason only if the value at the base is less than one if you increase the power the value would reduce had the value been more than one to reduce the value the power has to be reduced since the value here is less than one to reduce the value from 0.32 to 0.3 the power has to be increased so the next higher option for five years is five point four years approximately have you understood have you understood so five point four years is the answer you have to be smart and solving such questions i told you what guys always pick them what moderate options don't plug in 4.5 years and waste your time amongst 4.5 5 and 5.4 which is the moderate option 5 is a moderate option always do that for pi you're getting the value more it has to be reduced obviously power has to be increased why the base value is less than one the power is increased then only the value will reduce and it will match up to 0.3 have you understood everyone guys is it clear is it clear everyone yes okay let's move on to the next question a is equal to thousand n is equal to two r is equal to six percent compounded half yearly conversion has to be taken care of what is n for half yearly compounding two into number of years how many years they have given 2 so 2 2 4 i is equal to how much percent 6 percent means 0.06 how many 2 that means 0.03 now what is that we need to find ci or amount principle so what connects amount and principle tell me a is equal to p into 1 plus i whole power n correct a is equal to p into 1 plus i whole power n guys if you want to find p where will 1 plus i whole power n go below now what you need to do type a first what is a 1000 have you typed a divided by press divided by button what is one plus i value 1.03 guys what is the power n 4. press equal to how many times n is equal to 4 press equal to only 4 times when you are dividing it please remember when dividing how many ever is the powers same number of times you have to press equal to four times what is the answer eight eighty five is that the answer everyone got that's okay guys is that the answer once again amount is how much 1000 pressure divided by what is 1 plus i value 1.03 whole power what is n 4 press equal to how many times four times you have to divide press equal to four times guys understood have you first of all understood why we use this formula triple eight point check once again a is 1000 divided by 1.03 press equal to how many times four times huh triple eight point four eight the nearest answer only has to be ticked actually eight eighty five is very close to eight eighty eight that that approximation is always allowed what is that they have given in the key ansys so nearest answer see the difference is only three right so that can be ticked first of all it's their mistake it should not be 885 it's 888 point something it's wrong first of all option is wrong to justify their answer mistakes so they have given 885 as the right answer a lot of mistakes so i i i say that don't do it the exam that those things will not happen don't worry would you worry about exams one or two mistakes will happen because rehearsal you know okay next question guys the population of a town increases every year by two percent of the population at the beginning of that year okay that means what is i two percent that means 0.02 number of years by which the total increase of population will be 40 total increase means interest rate guys what do you mean suppose uh you have invested ten thousand and that has become for fourteen thousand correct ten thousand becomes fourteen thousand what is ten thousand principle what is the fourteen thousand amount what is the increase in the value four thousand so what is that four thousand according to this interest rate so here increase in the population is forty percent so isn't it an interest isn't it obviously right increase in population or increase in population is obviously what interest that is ci understood understood okay everyone is it clear the concept increase in population means it is extra thing extra thing is what always in ci it is ci only right extra thing is only ci yes now listen total population should become what in that case p plus 0.4 times p 40 percent of obviously 40 percent of p right 40 percent they have said 40 of what the principle so the interest that you get is 40 percent of the principle so can i write this as a is equal to 1.4 times p so what is this 0.4 p tell me first of all it is c i right you know amount is p plus c i yes or no amount is p plus c i yes or no so c i is zero forty percent of principle that is zero point four times p so can i add and write it write this as one point four p i can do this okay now guys a is equal to 1.4 p you understood now tell me what is the formula in case of a ci that connects amount and the principle appreciation formula what is it a is equal to p into 1 plus i whole power n clear now in place of a can i write 1.4 p p now 1 plus i will be 1.02 yes or no whole power what n p p cancels now you know how to do this 1.02 in the calculator you have to feed keep pressing press into keep pressing equal until you guess what you get 1.4 approximately even if it is 1.39999 it is 1.4 only counter number is 18 actual power is 17 the answer for this question is option c counter number is 18 so actual power is 17 therefore the answer is n is equal to 17 have you all understood haven't noah okay what they've said in how many years the total increase in population will be 40 percent 40 percent the population increases means it's an extra thing right what is the extra thing in case of component is ci only is extra thing right so i have written amount as p plus c i basically a is equal to p plus c i so what is c i 40 percent of what principle so what is 40 means 0.4 b so that means a is equal to what p plus 0.4 p is 1.4 p okay you understood this now since we have amount and principle equation what connects amount in principle a is equal to appreciation formula p into 1 plus i whole parent in place of a it's 1.4 p p p cancels so 1.4 is equal to 1.02 whole parent guys these kind of equations are always easy by type 1.0 to press into keep pressing equal until you get this left hand side value for counter number 18 you get 1.4 closest to 1.4 so obviously the actual power is 1 less than that so n is equal to 17. have you all understood online students have you all understood please do respond these are all laddu questions guys right straight questions no we don't like laddus make it boondi and eat [Music] huh right let's move on to the next question now let's see what kind of equation 3 year difference a 2 year difference you know the shortcut for 3 difference yeah 110.16 divided by i square into is it only i square three plus i tell me now the answer huh shortcut three-year difference is given what is the rate of interest given six percent mean zero point zero six huh what was the answer ten thousand how many seconds high seconds if you can identify it's a three-year difference question repeat the three-year difference in the calculator so what is the shortcut actually difference for three years difference for three years divided by what i square into three plus i have you all got ten thousand have you all got ten thousand give it to me fifty thousand only you did not give that's okay but at least ten thousand it should give me no ah small amount clear guys doubter everyone is it 10 000 is it 10 000 understood okay look at the next question the useful life of a machine is estimated to be 10 years what is it n the cost is 10 000 rate of depreciation is 10 percent the scrap value yes tell me scrap value means p or a hey what is given to us 10 000 p p what is that we need to calculate a so what does depreciation formula p into 1 minus i whole power n guys for 1 minus a what do you do 1 is taken as 100 i is 10 100 minus 10 is 90 90 means 0.9 raise the power to 10 that means counter number is 11. 0.9 raise the power to 10 into p which is 10 000 answer is three thousand four eighty six point seven eight guys one step nothing to be written on paper have you understood i'm not getting uh ten thousand for the previous question huh yeah javier you can uh do the calculation now what is given to us 110.16 is the three year difference right so what is the shortcut for finding out principle when the three year difference is given p is equal to difference for 3 years divided by i square again divided by 3 plus i so type 110.16 first have you typed it press the divide by button yeah and i square what is i value 0.06 typed it square means how many times you have to press equal to two times okay you've done that then what do you do with 3 plus i would you multiply or divide would you multiply or divide divide why because it's in denominator pressure divided by button what is the value of 3 plus i i is 0.06 means 3 plus i is 3.06 now don't you get 10 000 now yes what was the mistake that you were doing earlier i think you were multiplying three plus i know um where's got the answer okay look at the next one the effective rate of interest corresponding corresponding to a nominal rate of seven percent per annum converted quarterly seven point one eight what is the first thing that you would do conversion what is the conversion n is equal to 4 into number of years for effective rate of interest number of years is always 1 so it is equal to 4 what is i 7 means 0.07 divided by what 4 and that is 0.0175 now percentage eri is 1 plus i whole power n minus 1 into 100 what is one plus i guys one point zero one seven five because when one is added one will go to the left of the decimal type one point zero one seven five raise the power to what four you know how to raise the power to four press into keep pressing equal until the counter number is five then minus one then in 200 answer is 7.18 guys what is very important thing for effective rate of interest or ci problems the conversion that's the key if you don't do conversion the problem will go wrong problem will remain as a problem only yeah have you all understood i don't know how to solve and calculated that how to raise a dikshita listen to me now okay listen to me type 1 plus i now what is 1 plus i 1.0175 you type it please respond at each and every point that i explain you say yes or no type 1.0175 because 1 plus i is 1.0175 isn't it is there a doubt in that how one 1 plus i is 1.075 because i is 0.075 0 175 when you add 1 to it it will go to the left of the decimal point it will become 1.0175 is it clear so have you typed 1.0175 okay now you need to raise the power to what four right press into press into and keep on pressing equal until the counter number here is how much five pi y because the actual power is four it should be one number more than actual power so what is the value you are getting you will get some value right tell me what is the value what is that value i want you to tell the value 1.035r is it i think dikshitar your calculator has an issue you did not tell me that only first in some calculator after typing 1.0175 okay after typing one point oh i think you did not type one point zero one seven five dikshita it's one point zero one seven five please type it the value of one plus i is one 1.0175 then press into and keep pressing equal until the counter number is 5 please do it so same answer i mean when you're pressing equal to the value is not changing or changing press one more equal to is it the same value please respond quickly press one more equal to same only so that means your calculator has an issue why didn't you tell me huh so in that case what you need to do let me tell you see you you need to type 1.0175 okay if you have if you have told me this problem i would have given the solution earlier only in some calculator by pressing into only once the power doesn't change after square so you will have to press into twice now you do it after typing this 1.0175 press into twice press into twice and keep pressing equal but this time remember when you press into twice the counter number should be two numbers more than actual power so it should be six now tell me guys tell me is the value changing now by pressing equal to after into twice is the value changing now by pressing into twice yes now counter number should be how much to number more than actual power but i'm saying okay not for everyone okay now what you do after that yeah yeah minus do minus one then into hundred finally seven point one eight got it i'm happy enough got it so dikshitar here after going forward you have to press into twice for raising the power and counter number should be two more than actual power please remember and i'll not be repeating again and again because yeah you understand okay guys please solve this question what type of compounding of early huh what is n for r f really 2 into number of years what is number of years guys 1.5 right so what is n 3 years what is i 0.1 divided by 2 which is 0.05 what is asked ci quickly guys p into one plus i whole power n minus one one point zero five press into digital has to press into twice answer two five two to a option b the you'll have to press into twice now and take the counter number more than two more than actual power power is three so counter number for you should be five all right and then minus one and then minus one into p p is how much sixteen thousand is that two five two two everyone yes let's move on to the next question ci on 40 000 at 10 per annum for one year when the interest is payable quarterly guys again led to question n is equal to what what type of compounding quarterly 4 into how many years they have given 1 year and that is equal to four i is equal to how much percent ten percent zero point one divided by four zero point zero two five so ci option see here answer is 4152.51 option c should i explain the calculation guys okay next question guys the difference between ci and si for 2400 for two years at five percent per annum guys how many years they have asked difference two years so if you remember the shortcut that i have given for two years what was it p is equal to difference for two years for two years divided by what i square but what do we don't know here difference we don't know what do you do to find a difference cross multiply p into i square that's it so difference is equal to p into i square what is p guys 2 400 what is i 0.05 again into 0.05 how much answer is f6 understood so this shortcut is not only to find the principle you can even find the difference also when the principle and i is given understood multi-purpose shortcut understood all right guys understood in the problems earlier they used to give difference they used to ask what principle this problem they have given principle they asked was to find what difference what do you do cross multiply p into i square that's it difference between c i and s i for two years shortcut so it's a multi-purpose shortcut you can solve two varieties of questions understood foreign i don't know whether i made a fright state i use the right word or not okay next question the annual birth and death rates per thousand guys please concentrate on this question everyone the annual birth and death rate per thousand per how many per thousand clearly they are specified per 1000 people how many will die how many will take a birth 39.4 how many will die out of how many thousand out of thousand the average number of people taking birth is 39.4 and average people taking i mean dying is 19.4 and the number of years in which the population will be doubled guys double means what a is equal to 2p correct a is equal double means a is equal to 2b b its simple interest or compound interest it is a is equal to 2p double means now tell me population problems are always ci problem or si problem ci problems correct ci problems now guys tell me what connects amount and principle in compound interest appreciation formula p into 1 plus i whole power n what do i substitute in place of a to p p p cancels and what is i we don't know tell me to find i what is i basically rate of growth of population how do you calculate that guys population is calculated for on based on number of people taking birth and number of people dying it is based on what how many people survive right exactly see population is calculated growth is calculated based on what how many people survive yes or no so how many people survive 39.4 minus 19.4 taking birth and dying out of how many thousand it is not out of 100 it is out of thousand tell me what is i zero point zero have you understood what is high how to calculate i everyone uh what's the model of your calculator mj 12d you can you can see you can get this one also this is also fine other than ct 512 wt mj 12d is also fine is there any other model offline students using dg dg one two pier yeah you can use this also mj 12 d also ct triple five okay bhavia bharati did not understand the calculation okay which calculation the last one uh yeah last question listen listen listen i'm doing the marketing for the calculators okay right uh look at the question what is the question the annual birth and death rates per thousand please listen to me per thousand out of one thousand the average number of people taking birth and average number of people dying is 39.4 and 19.4 respectively the number of years in which the population will be doubled what do you mean by double a is equal to 2p because it is double they say right okay now population problems is always what ci correct so what connects amount in principle in case of a ci appreciation formula so a is equal to p into 1 plus i whole parent all right all right okay now without knowing i value we cannot find out the required stuff right so how do you find i basically what is i for population problem population growth so growth is calculated on what is it on only number of people taking birth or number of people dying no it is on based on how many people survive so how many people survive 39.4 minus 19.4 out of how many thousand so population growth rate is 0.02 35 years is the right answer very good okay now 1.02 will be 1 plus i whole power n guys you know how to solve such questions type 1.02 in the calculator press into keep pressing equal until you get 2 or 1.99999 what is the counter number 36 so actual number is 35. ah dikshitar you have to type 1.02 press into twice and keep on pressing equal until 2 appears in the calculator and you will see the counter number is 37 so therefore the answer is 35 for you i mean everyone it is 35 only but the counter number should be 37 for you all right guys is it clear so far everyone done with the questions on ci tell me questions in icm material are easy or questions i solved are easy i see a material question but the questions which i explained the concept which i explained that is what is required for the exam okay you understood so i say equations are always easy right but the question they'll ask will not be the questions from your ica material few 10 to 15 questions they would pick and place it not from this chapter overall only 10 to 15 questions will be as it is from your exercise but remaining 85 questions so they can ask any question so why i said concept is the key the shortcut is the key guys are we clear so far are we clear so far shall we move on please concentrate because the next concept is very very important equally important as you dealt with what simple interest and compound interest and duty is easier compared to simple interest in the compound interest for the fact that you don't have much types in annuity you don't have much types you have four formulas that's it for four formulas if you remember one remaining three formulas easily you can get it how to get it that i'll tell you don't worry so it's all about those four formulas in annuity you know that your annuity is done first of all let us see what is annuity guys please do concentrate this uh before i define annuity i would like to give you an example okay let's say let's say you have taken a rental house what rental house okay say the agreement that is made between you i mean the tenant and the owner says that for 11 months the agreement is usually the rental agreement will be for 11 months and the rent agreed between the tenant and the owner is say 10 000 per month 10 000 per month now tell me within this 11 months will this change no it will be 10 000 only when do you pay this 10 000 only once only once no this should be paid regularly every month for next 11 months it's not that after 11 months it's a free no again the rental agreement will change the owner will increase the rent of maybe five percent depending upon the inflation rate right yeah okay obviously there will be a hike in the rent so this 10 000 what you pay isn't it a regular payment isn't it a fixed amount ten thousand it's not like ten thousand you pay this month and twelve thousand you will pay since you got more salary no right even if you got more salary also you'll pay only ten thousand right so ten thousand is what is called as annuity 10 000 is what what is it it's a fixed value and you're gonna pay it regularly you're gonna pay it regularly for specified number of periods how many periods 11. in this example it is 11s it could be 12 years or maybe 10 years or maybe 15 years or maybe 5 years it could be any number of periods for this example it is 11 periods so this 10 000 whatever fixed amount that you pay regularly for specified number of periods in this example the specified number of periods is 11. you understood what is annuity so annuity is a fixed amount a fixed amount paid regularly for specified number of periods is not a principle principle is one time fixed principle is what suppose you invest one lakh in the bank is it repeated is it a recurring deposit no if it is recurring deposit yes it is annuity it can be said as annuity if it is a fixed deposit it is never an annuity the deposit what you pay right what you keep in the bank that should be recurring you understand what is recurring regular it should be regular once in a year or once in a half year once in a month it should be repeated if it is recurring then only you say that is the annuity if it is only one time let's say you invested 5 lakh in a bank for 5 years are you going to invest 5 lakh every year or every month no right it's one time so that is just a principle that said that is not the annuity you understood the difference between the principle and the annuity everyone online students yes or no guys my god what is annuity a fixed amount paid regularly for specified number of periods so what are the examples for where do you come across paying fixed amount regularly for specified number of years rent is an example what else emi emi is an example yeah salary is also yes let's say for this particular year your salary is fixed you get a regular payment so that is also an annuity yeah you can say because for one year i mean for one year it is fixed but after one year it will change just like a rent so it's also annuity how about dmi emi is an annuity how about insurance premiums that is also annuity it's a fixed amount paid it could be once in a year once in a quarter once in a half year that is also what fixed payment for specified number of periods you understood recurring deposit rd rd account have you heard of hardy accounts that is also what repeated payment regular payment only for specified number of periods that is also an example for annuity now those annuities can be further divided into annuity regular and annuity due there are two types of annuity one is annuity regular the other one is annuity due this regular annuity is also called as ordinary annuity so what is ordinary annuity or regular annuity we will see okay a fixed amount a fixed amount paid regularly at the end of every year at the end of every year or every half year or every quarter or every month if the payment is made at the end of every year or at the end of every half year or at the end of every quarter or at the end of every month you say that as what annuity regular now tell me guys paying a rent is it a regular annuity when do you pay the rent yes that's what you pay the use you'll say that i'll pay the rent in the starting of the month right but when do you pay the first rent is it the first day when you take a rental house no you pay the rent after one month that's what the meaning of end of one month you understand you understood the word understood the meaning of end of every year end of every month end of every quarter means after one period only you're gonna pay it when you take a rental house okay when you take a rental house when do you pay the rent first rent after one month yes you say i'll pay the rent on first off every month that's okay but when it is that when when are you paying that after one month only right after one month means at the end of one month only right so that is annuity regular how about emi guys when you take a loan from the bank okay the first tmi starts when that particular day or after one month no no no after one month only the first emi starts so loan will not loan emi will not start on the that particular day itself let's say you're taking a loan of 5 lakhs okay you have to pay every month 12 000 rupees the first emi start will commence the end of one month after one month only it will start it is not that very first day okay so paying a emi paying a rent is all are all what annuity regular so what are the examples rent emi are the examples for what annuity regular guys is it clear so far is it clear so far now let us see annuity immediate or annuity due so what's the difference between regular interviewers here also you pay a fixed amount fixed amount paid regularly at the beginning of beginning of the beginning of a beginning of an year of a year or beginning of half year or month or quarter sometimes starting from today starting from today if they say starting from today that is annuity due or annuity immediate understood the difference annuity regulator is at the end of the every at the end of every year at the end of the half year at the end of the quarter at the end of the month annuity due is at the beginning of the year at the beginning of the half year at the beginning of the quarter at the beginning of the month or starting from today or starting from today so where do you come across annuity immediate or a due guys how about insurance premiums when you take an insurance policy the first premium has to be paid the first day that particular day itself so it is annuity due where else guys if you open a rd account recurring deposit account in a post office let's say so when you have to pay the first investment that particular day itself when you open the rd account the first investment has to be made recurring deposit has to be made that particular day itself so rd even for bank account also so rd is an exam but bank account it's one time you deposit right yeah that is principle that is principle recurring deposit is different fixed deposit different in fixed deposit there is no repeated uh invest payments or only one time payment right recurring deposit let's say 10 000 every month so you'll you'll be paying 10 000 once in a month that is annuity principle is not an annuity please get that point principal is not an annuity principle is only one time investment recurring deposit is an annuity repeated investment regularly and a fixed value right so rd is an example for annuity or immediate and one more what is that i said insurance premium insurance premium guys are we clear so far are we clear so far everyone clear please tell me yeah shall we move on okay let's get into the business end of this annuity chapter now we got the concept word of water's annuity now let's see you saw what are uh the different types of annuity what are different types of vanity and you d regular or annuity you got the difference what is annuity regular or annuity ordinary annuity whenever the payment is made at the end of every year end of every month end of every quarter end of every half a year it is annuity regular or ordinary annuity if they specify the payment is made commencing now or starting from today or at the beginning of every year the beginning of every half year quarter of beginning of every month then it will be annuity immediate yes now tell me in case of uh compound interest if they don't specify about the type of compounding the default compounding is which one yearly that is annual compounding so here also we have a default annuity the default annuity what you mean by default if they don't specify when the payment is made at the beginning or at the end if they don't specify about that the default annuity is regular annuity please understand the default annuity is what regular annuity i'll specify that later first we'll see future value of an annuity guys i'll go back to the example of a recurring deposit okay so what what happens in recurring deposit let's say you invest 5000 repeatedly every month for next three years let's say after three years how much is the annuity in this problem three thousand three thousand is the annuity why it is called as annuity because it's a fixed amount paid regularly for specified number of periods all right 3000 is a fixed amount that you pay regularly for specified number for 3 years 3 years means 3 into 12 36 months it's a regular payment a fixed payment for specified number of periods after three years that is 36 months you get a lump sum amount what is that lump sum amount whatever you invested along with that interest has been added will be added so you get a lump sum amount when do you get that lump sum amount in the future and that value will be future value of your annuity you understood you paid the fixed amount regular payment for specified number of periods for which you get a lump sum amount in the future is it today no in the future that is called as future value understood let's say in the future you got you received five lakhs you received five lakhs so is that file x and today's file acts the same no which file act will be more value will have more value today's 5 lakh or 5 lakh after uh three years today's file act will have more value why phi lakh after three years will have lesser value because because of inflation rate the value of money will decrease understood is it clear okay so that is what the meaning of future value and present value future value means in future what is that you're going to get for your annuity suppose if it is 5 lakh today what is its equivalent value that is present value so you'll be you'll be dealing with only future value and present value in this annuity concept that's it only future value present value that's it let's see what is future value it if a is small a means what the small a is what the fixed amount paid regularly for n number of periods at the rate of i percent per annum then its future value is given by see future value again there are two types one is future value of annuity regular other one is future value of annuity guys uh there is a formula actually uh before giving before me giving this formula i would like to explain how to get it in simple way okay guys fv of a r a r means what and new d regular here onwards we would not say annuity regular we say ar for annuity you will not say annuity due we say a d f future value will not say future value f v present value will not say present value pv all right okay now guys for future value of a r just remember three terms just remember three terms the three terms is a into e r i divided by i only these three terms you know what is er is effective rate of interest you know what is i is nominal rate of interest what is a a fixed amount that is annuity when an annuity is multiplied with effective rate of interest and then divided by nominal rate of interest you always get the future value of annuity regular now guys if you remember these three terms to get the expanded formula of fv of ar will be very easy how guys you know what is eri right what is eri 1 plus i whole power n minus 1 remember this eri is not a percentage eri it's just a fractional eri okay just divided by i so this becomes fv of a r so you need not by heart the formula as it is just remember three terms e into e r i a into e r i by i you can always replace for e r i and you get the expanded formula so so i a into 1 plus i whole power n minus 1 divided by i have you all understood have you all understood how to get this in one step i mean if you need not by heart this you need not by heart this you can easily get it by remembering only three terms a e r i by i all right what is small a here please don't get confused between that capital a and the small a in your icm material they'll give you capital a only for annuity so to avoid the confusion i made it small a because that a and this a shouldn't get confused okay that capital a is the amount future value it is this only is the annuity the fixed amount so why i made it small a to avoid the confusion all right okay now if you have understood what is fv of annuity regular let us see what is fv of annuity guys before giving you the formula i would like to explain something that helps you to remember how to get the formula for fb of 80 please concentrate first of all guys in case of annuity due so first of all tell me in case of annuity regular if it is four year investment how many years let me let us let me make it as three years instead of four years okay if it is three year investment when do you make the first year investment is it beginning or when at the end of so let's say 10 000 is what you're gonna pay every year at the end of second year also ten thousand at the end of third year also ten thousand this is what happens in case of annuity regular and this is what the formula for fv of ar but in case of annuity due for three years what is the first payment when do you make the first payment starting what is the difference guys here you for the first year would you get the interest you are not you're not actually paying anything for that right for example rent let's say as and when you you give the rent uh your owner will give it to someone for the interest he'll invest that amount as for the interest okay so will he get uh let's say 10 000 rupees is what you're gonna give to the owner as a rent and he's going to give it for 10 per month okay on interest basis so he'll get how much every month 1000 rupees extra for his rent will he get this 1000 rupees extra interest for the first month itself no when will he get after you give 10 000 then only he'll invest then only he'll get right suppose if you make the first payment the first day itself he will invest straight away and he'll get the interest right so but here in case of an annuity due you are paying the first payment that particular day itself so for this 10 000 for this first one year the interest has to be included extra interest has to be included whereas for this for the first year no interest you're understanding the difference between regular and you for the regular payment is made at the end of one month or at the end of one year at the end of half one quarter or at the end of uh half a year so obviously for the first payment the interest is not there for the first time duration right whereas in case of it annuity due the first payment obviously the interest when why the interest has to be added because the first payment is made today only yes or no the interest will start from today only right whereas for you i mean regular the interest will start at the end of that particular period after one month or after one year after one half a year or after one quarter only the interest will start counting right but here due interest will be counted from the day one so for this 10 000 whatever you're paying the interest is calculated from day one so one year difference is there one year extra interest you should get in case of annuity you so why if you remember the formula for annuity regular the same formula the same formula you have to write what is it a into 1 plus i whole power n minus 1 divided by i what is this formula guys fv of ar annuity regular only thing is that you need to multiply with this is 1 plus i so this will take care of giving you the interest for your first payment whatever the first payment you made for that interest is to be taken care of right so this one plus i will take care of that interest you understood so what is the extra term that you have to include for annuitu same as annuity regular formula only into one plus i you have to do so you get the formula of fv of 80. so what i told you there are four formulas if you know first one easily you can get the other three formulas have you understood have you understood everyone sir if if the payment is regular and the amount is varying can it be considered as no no no if the payment is regular and the amount is varying it is not the annuity what is the condition for the annuity it should be a fixed amount it should be a fixed amount unless it is a fixed amount it is not an annuity it's a it can be considered as the compound interest because principle the investment is changing so that is not that doesn't come under annuity is that clear uh bhavia asked right very good very good doubt is that clear so that is not considered to be annuity what is the definition of annuity it's a fixed payment made regularly for specified number of periods if the payment is not fixed it is not all right okay so you got the difference between annuity regular and android u in terms of formula what is the extra term 1 plus i to be multiplied where in the numerator or denominator numerator so tell me fv of a d will be more or fe of a r will be more a d will be more because extra interest obviously a d will be is it clear everyone guys are these formulas clear so far shall we move on okay now relationship between future value and present value guys you need not by heart this forget about this formulas why i'm saying you need not by heart this let me explain okay so you know what is appreciation formula what is appreciation formula a is equal to p into 1 plus i whole power n correct if you know appreciation formula getting the relationship between future value and present value is very easy why because guys amount when do you get the amount for your investment in future so this amount itself is future value when do you invest guys today so that is present value so fv is equal to pv into 1 plus i whole power n isn't it fv is equal to pv into 1 plus i whole power and if you remember appreciation formula you can get the relationship between future value and present value am i clear am i clear guys everyone now so how do you find pv then fv divided by 1 plus i whole power n just the rearrangement of terms that's it you understood you understood how do we what is the base for relationship between future value and present value appreciation formula everyone clear shall we move on yeah now let's see having seen a future value of annuity regular and future value of annuity you let's move on to present value of an annuity yes already i told you in future if you're getting some amount what is its equivalent present value that is what is called as present value of an annuity let me give one example guys let's say if you are in need of a loan of five lakhs okay you apply for a loan and you get a loan for which you're going to pay the emi what is that emi called as annuity you're taking a loan of 5 lakhs i'll just write down you've taken a loan of 5 lakhs all right and the emi fixed for that is 12 000 every month per month for five years okay what is this twelve thousand what is this twelve thousand annually fixed amount so it is annuity a what is this five lakh uh-huh when did you take the loan in the future so you're not a time traveler right you have taken a loan today only right you have taken a loan today so you obviously it's the present value of future value obviously it is pv of annuity right present value of the annuity for this present value you are going to pay the emi and that is annuity a you understood so always please understand whatever loan that you take the amount that you take from the as a loan that is always present value am i clear for loan problems always apply present value concept am i clear everyone online students guys is it clear yeah so let us see the remaining two formulas of annuity that is present value formulas okay what is present value it's a fixed amount to be paid regularly for n number of periods if a is a fixed amount paid regularly for number of bits you assume a is what emi then its present value now present value means there are two types could be annuity regular or could be annuity due guys if you know this relationship between future value and present value getting pv of er is very easy what is it pv of a r is equal to fv of a r because what is pv fv divided by what 1 plus i whole power n divided by what 1 plus i whole power what is fv of a or already we know a into 1 plus i whole power n minus 1 divided by what i this is what fe of a r and extra thing is what 1 plus i whole power n where it should be in the denominator only so into 1 plus i whole power n so this is the formula for pv of ar if you know fv of ar it's a into 1 plus i whole power n minus 1 divided by i extra thing in the denominator should be what 1 plus i whole parent how did it come from where did it come from from the relationship between pv and fv where did this relationship come from appreciation formula is it clear it's not coming from no i mean from moon or from mars or anywhere it is their only appreciation formula that's it is it clear yes is it clear everyone yes so if we know fv of a r can't you get pv of a r you can what is the only thing that you have to do in the denominator 1 plus i whole power n you have to divide that is it is it clear is it clear so let me show the formula over here what is the extra fitting here 1 plus i whole power other than that everything is same as fv of a r should i write pv is fv divided by 1 plus i whole power n it's understood right now the next thing present value of annuity due all right let's listen before i give you that formula i need to explain something okay please concentrate if you understand that concept remembering the formula i mean remembering the formula it's not a big deal why the formula takes that shape that is very important okay so first of all listen to me guys what are you finding out present value of annuity due present value of annuity let me talk about present value of ar for a while okay ar means let's say you make three year payment 10 000 at the end of first year 10 000 at the end of second year 10 000 at the end of third year so basically present value of this annuity means this 10 000 when are you paying after one year what is its present value will be less or more lesser then again ten thousand next ten thousand when are you paying after two years what is its present value that you will calculate what what is this ten thousand it's a future value when do you pay this after three years at the end of three years that present value also you will calculate then you add them up to get the effective present value of this annuity you understood that is what is happening in this formula that is what will happen in this formula if you use this formula this is what is going to happen what 10 000 is the first annuity first annuity when do you pay it at the end of one year what is its present value lesser than that some value you will get 10 next 10 000 when you pay after two years what is its present value that will that you will find out this 10 000 is at the end of three years what is its present value you will find out you will sum them up you get what effective present value of this whole annuity so that is what you will be finding out using this formula this formula actually will do that i told you i mean theoretically how it works so by using this formula this is what exactly is gonna happen if you do use this formula is it clear now tell me guys in case of annuity due when the first payment is made today only second payment third payment here all right now guys what happened here you converted this 10 000 to present value you converted this 10 000 to present value you converted this 10 000 to present value then you added up that is the present value of the overall annuity now tell me guys is it required to convert this 10 000 to a present value that itself is a present value is it required for this is a conversion required for this no conversion required conversion is required for only these two payments if there are n payments the conversion is required for only n minus one payments why n minus one the first payment itself is the present value no conversion is required you understood the conversion is required for only n minus 1 payments is it clear if you remember the formula of fv of a r for fe of a d the same formula but in place of n it will be n minus 1. that will do convert whatever this the second payment then third payment into present value and then this value to be added to get the effective present value so now if you if i give you the formula it will make sense to you please understand now i'm going to give you the formula now you will understand why the formula has taken the shape let's what is this plus a fixed amount why have i added plus a here present value of what why this plus a comes in here see why do we have n minus 1 in place of n for the first payment we don't do the conversion if there are n payments the conversion has to be made only for n minus 1 payment so wherever n in this formula the same formula but n is replaced by what n minus 1 in this then why why do we have plus a the first payment okay guys 10 000 10 000 let me write ah that does it you got it now see 10k 10k 10k you make the conversion for these two payments that's it right you make the conversion only for these two payments if there are n payments you make the conversion only for n minus 1. so this will take care of that conversion for this and this whereas for this this has to be added as it is so y plus a what is a basically annuity who understood the formula why it has taken the shape everyone what sort of annuity it is annuity due and what value is it future value present value present value have you understood everyone guys you understood please tell me is the concept clear uh i already told you what default annuity is what regular if they don't specify when the payment is made at the end of the year at the beginning of the year they don't specify anything by default it is to be and first of all how do you identify the question as an annuity problem fixed amount okay then what else should be there to identify the question as an annuity they have to specify rupees 10 000 invested every year rupees 10 000 invested every month yeah specified number of periods it will be there but every month every year every quarter every uh half a year that you have to see that will say it is annuity problem or not if it is not a regular payment it is not annuity problem am i clear how to identify any problem some amount invested regularly every year or every month or every quarter or every half a year it could be anything but it should be invested periodically regularly right then only it is annuity problem guys am i clear am i clear everyone okay we'll take uh one problem problems based on fvpv and relationship between future value and present value yeah before i give you uh the problems uh you have to remember what first of all relationship between future value and present value for relationship do you have to buy hat any formula no appreciation formula a becomes what fv p becomes what pv and into 1 plus i whole power and this is the relationship between future value and present value then what is f v of a are annuity regular i told you three terms to be remembered what is it a into e r i divided by i then you can always get the expansion of it what is eri 1 plus i whole power n minus 1 divided by i okay second one fv of a d guys what is the extra thing that you have to do here into one plus i to which formula f v of a r into one plus i you have to do f e of a d got it now a pv of what a r so pv of ar means same like fv of ar denominator will be having extra term what is the extra term 1 plus i whole parent that is a into 1 plus i whole power n minus 1 divided by i into 1 plus i whole power now tell me for fourth one pv of a d guys same like pv of a r this term will be there but in place of n n minus 1 a into 1 plus i whole power n minus 1 minus 1 divided by i into 1 plus i whole power n minus 1 along with that plus a guys these formulas are the key for you to solve the questions on and you t the rest of the chapter is there any difficulty in remembering this is there any difficulty in remembering this please do let me know if you know one getting other one other formulas are very easy difficult tell me is it difficult difficult or not difficult easy easy right i'll make it more easier by solving more problems oh sorry this is 80. [Music] understood we'll solve one example then go for break or what it's all examples huh now tell me what makes you say this is annuity problem every year that that wording you have to see to decide whether it is annuity problem or not what is annuity here 5000 is the annuity and 12 percent is i that means zero point one two for ten years that is n find what future value okay it's regular due how do you say regular have this specified at the end at the beginning they have not specified so by default by default it is what by default it is a r correct so what is that we need to calculate fv of ar correct fv of a r let's tell me the formula for fe of a r a into e r i what is e r i 1 plus i whole power n minus 1 divided by i do we have into 1 plus i whole power n for f v do we have 1 plus i whole power in the denominator for fe no it is only for pv right it is only for pv guys let me tell you how to carry out the calculations in one step in the calculator tell me according to priority what is the first thing that you would type within the smaller bracket what is one plus i one point one two type one point one two in the calculator everyone dikshitar will have to press into twice yeah hope you remember that into keep on pressing equal until you get counter number as 11 okay then what you do complete the brackets minus 1 then come out of the brackets into a what is a 5000 then divide press the divide by button i is how much 0.12 what is the answer 87 7 i think you did not divide you multiplied divided by come on guys you got the answers please do let me know got it any doubt with the calculations guys compared to simple interest compound interest this kind of equations are very easy no type nothing whatsoever only thing is that you need to identify it's an annuity problem regular audio you have to see future value of present value you have to see accordingly or to solve it that's understood understood everyone saw this then quickly first of all tell me what type of an annuity mr bhuvan invest rupees 10 000 at the beginning of every year for the next its annuity dues what is this 10 000 a yeah beginning of everywhere means 80 right for next 11 years find the present value of this annuity you have to be very careful pv of a d guys pv of 80 when you're finding out present value of a d n minus 1 comes or just n n minus 1 so it is a into 1 plus i whole power n minus 1 minus 1 divided by i into 1 plus i whole power n minus 1 just tell me is it only this much or you have to do something else plus a because it is pv of annuity due guys listen all of you listen all of you because there is a very important point that you have to remember when you do the calculation in one step especially this kind of calculations everyone please listen do the ins i mean do follow the instructions as i say according to priority what is the first thing that you should be typing whatever within the brackets 1 plus i guys i is how much here 0.08 correct 1.08 type 1.08 press into keep pressing equal until n minus 1 guys n is 11 n minus 1 is 10 so your counter number should be 11. so n minus one is actually ten huh wait wait don't do minus one wait wait see you got one plus i whole power n minus one right that value you got something right that value again you need it for the denominator yes or no 1 plus i whole power n minus 1 is there in the denominator as well especially if present value problems please understand whatever is in the numerator the same thing is in the denominator as well 1 plus i whole power n that has to be stored m plus have you pressed m plus to store the value then what you do 2 minus 1 done minus 1 come on minus 1 minus 1 2 minus 1 okay then press the divide by button press the divide by button what is i 0.08 then would you divide or multiply d y because it's in denominator divide where is this value guys in the memory how do you recall mrc right press equal to press equal to then into a into 10 000 then plus 10 000 what is the result hundred point eight one seventy seven thousand one hundred point eight one again sure sure sure sure there's no hurry okay right please concentrate please do concentrate here n is equal to 11 so what will be n minus 1 10 all right n is equal to 11 so n minus 1 is 10 okay now what is the first thing that you have to type 1 plus i what is 1 plus i 1.08 now power 10 right because n minus 1 is 10 raise the power to 10 that means counter number should be 11. now after raising the power to 10 please understand this 1 plus i whole power n n minus 1 should be required for denominator also what you do store it if you store it you can always recall it right store it by pressing m plus then do what minus 1 continue doing the calculation as it is minus 1 then press the divided by button what what is i 0.08 type 0.08 then this value would you have to multiply or divide divide y because it is in denominator press the divide by button and where is this value 1 plus i whole power n minus 1 in the memory how do you recall press mrc hope you are doing it then press equal to then into what guys after brackets next priority goes to multiplication or addition multiplication don't do addition i told you the priority is right after the brackets the next priority should go to multiplication so why into a first what is a ten thousand then plus a which is ten thousand don't you get seventy seven thousand one hundred point eight one have you understood everyone is it clear is it clear everyone so the rest of the chapter will be like this only you have applications of annuity but you will be applying either future value or present value okay so we'll go for break now we'll have 15 minutes break [Music] yeah so guys uh are these concepts clear future value of annuity regular future value of annuity present value of ar present value of 80 are these things clear so far online students please do let me know clear all clear yes okay shall we continue with the problems the refrigerator cost rupees 40 000 today then what would be its cost at the end of two years if the rate of interest is six percent per annum future what is that 40 000 today's value so is it an annuity problem it's a problem based on what future value present value relation correct so what what is this 40 000 present value what is that they're asking fv what is the relationship between fe and pv appreciation formula guys a is equal to p into 1 plus i whole power n you can use appreciation formula only right so fv is equal to pv into 1 plus i whole power n what is 1 plus i guys 1.06 raise the power to what how many is 2 years into what pv what is pv given 40 000 what is the answer huh 44 9 444 is the answer guys into 2021 december paper they asked three questions on this only relationship between future value and present value three questions they had asked so what's the mistake the student does is they'll apply annuity concept what makes you stop to apply annuity concept tell me every year that regular payment is not there in the question right today 40 000 the cost is 40 000 today that's it how they said every year forty thousand no so this is not annuity problem there's a relationship between future value and present or appreciation formula clear everyone that's clear tell me next question if a car cost rupees 20 lakhs after 10 years what is 20 lakh after 20 years it cost 20 lakhs guys this is what future value then what would be its today's cost if the rate of interest is seven percent per annum what is that we need to calculate present value guys what's the relationship fv is equal to pv into one plus i whole power and therefore pv is fv divided by 1 plus i whole power and guys no need to write anything on the paper what is that you type first fvfv is how much 20 lakh type it press what divided by press what divided by what is one plus i one point zero seven and press equal to how many times ten times press equal to 10 times otherwise find out 1 plus a whole power 10 and write down the value that you can do yeah find out 1 plus i whole part 10 press m plus then future value by denominator once again 1 plus i is what 1.07 press into keep pressing equal until 11 appears then what do you do with this store it by pressing m plus now numerator by denominator 20 lakh divided by what mrc press equal to what is the answer you got 10 lakh how much 10 16 698 ninety eight point five eight five eight is that the answer everyone got everyone online students yes clear ten lakh eighty seven ah come on once again you check what is 1 plus i 1.08 raise the power to 10 10 means the counter number should be 11 okay then what did you do press m plus right then numerator by denominator numerator is 20 lakh divided by mrc press equal to check once again check once again clear guys respond make it fast yes okay let's move on next sinking fund guys to explain what is sinking fund i'm going to give you an example okay say let's please concentrate you have a car okay you have a very good car the cost of this car is 25 lakh you bought this car by paying 25 lakh you know car is a depreciating asset correct it's a depreciating asset let's say the life of the car is 10 years let's say the life of a car is 10 years all right okay now tell me after 10 years what will happen to car it'll become a scrap it'll become a scrap useless scrap means what useless all right okay now once it becomes a scrap you have to buy a new car you have to buy a new car so obviously you will not come down to this quality right whatever car you are using let's say the same quality car the same model if you want to purchase what will be the cost of the same car after 10 years with the inflation effect taken into consideration it might even double also we never know right definitely it'll be huge compared to 25 lakhs right it'll be more than 25 lakhs just imagine arranging such a huge amount after 10 years in a single stretch is it possible it may be possible for some people it obviously it's not possible to arrange a huge amount in a single stretch right so you know that it's going to become a scrap after 10 years okay so from today only or maybe a regular payment if you start investing on that for that you are anticipating what you are expecting that your car is going to become a scrap after 10 years for that you are accumulating money it's not like you're keeping money in your what about locker no you're investing if you keep it in a locker what happens in your in your home it will not grow if you invest only it'll grow right with interest right if you keep it at home only the value of money will will decrease right there's no compensation for your money only right so obviously keeping up keeping with us only is of is not a good idea what do you do you invest okay so let's say you you you are getting a salary of one lakh out of that one lakh every month are investing 10 000 10 000 10 000 for the next 10 years so by the end of 10 years you get a lumps of amount along with the interest and with that you can buy a new car so for the future you are investing a fixed amount fixed amount for specified number of periods here in the example how many years i say 10 years right so it is basically sinking fund problems are basically future value problem for the future you are investing you are expecting something is going to happen in the future for that you are investing from whatever income or whatever profit you are getting from your business you are investing a part of it a fix as a fixed amount regularly and by the end of 10 years you'll be ready with the lump sum amount so you can easily purchase a new car understood so what is sinking fund basically it's a fixed amount only again guys sinking fund is what it's a fixed amount to be kept apart as an investment from the income or a profit in order to what accumulate a lump sum amount required for the future so i in in my example to purchase a car that is that is why you need a lump sum amount for the future right so you start investing fixed amount regularly for specified number of periods so in the future you'll be ready with that amount so you can purchase it understood what is sinking fund so sinking fund isn't it an annuity yes it is an annuity sinking fund basically what a fixed amount paid regularly okay for there's a purpose for it what is the purpose you need a lump sum amount for the future have you understood is it clear can you give more example for sinking fund yes let's say uh you have a credit of 25 lakhs and you have to clear after 15 years obviously arranging 25 lakhs is not possible in a single stretch so and say bank has given you a permission that after 10 year by 10 years you have to clear okay at the end of 10 years you want to clear 25 lakhs so arranging 25 lakhs in a single stretch is not possible so what you do for whatever profit that you get whatever income that you get from your business you start investing on that so that by the end of 10 years you'll be ready with that amount is that clear yes is that clear maybe yes so sinking fund basically means what it's a fixed amount it's an annuity only for some purpose there is a purpose defined for a sinking fund understood so sinking fund problems are always future value problems for the future only you're investing right is it not for the future only you're investing so always thinking fun problems are future value problems keep it in mind clear so the definition only it is that for future so definitely sinking point problems are future value problems is it clear guys is it clear everyone the concept of sinking fund so shall we have an example on sinking fund okay have a look arun wishes to buy a machine after 10 years after 10 years he wants to purchase a machine whose estimated cost is filak so what is filak value of future value read the question after five years he wants to purchase its estimated cost in the future is five lakh so this is what fv future value if the rate of interest for his investment is 8 percent per annum this is 0.08 which is high current okay find how much he has to invest every year how much he has to invest every year means it is annuity only and it is for the some purpose some purpose means it is sinking fund correct fv of ar or fe of ad annuity regular or annuity annuity regular why how investment okay is it regular at you i'm asking yes how come end of every year or end of every month i mean beginning of every year end of every year because they say what from your profit or income when do you get income after working for one month or working for one year right so it's a annuity regular and even if they don't specify by default what it is regular only right they haven't specified when the payment is made right so by default it is by default it is regular ar okay now fv of ar formula you are supposed to use what is fv of ar a into 1 plus i whole power n minus 1 divided by i correct 1 plus i whole power n minus 1 divided by i guys listen listen what do we know from this we know fv we don't know what a we don't know a guys in the calculation while solving some of the calculation tricks i explained something when you are finding out an unknown value you keep only unknown value on one side send everything else on the other side before sending everything else on the other side you have to solve that expression right and keep it in the memory yes or no yes or no so what do you first of all feed in in your calculator 1 plus i that is 1.08 raise the power to 10 that means counter number should be 11. then would you store that value no that is not required for denominator then do what minus 1 then do what i i is how much 0.08 guys if you know a you can multiply a because your a is only asked you are going to store this value why you are going to store this value because you are going to send this value to the left hand side as a denominator yes or no yes or no so what is fv of ar given pi lag so after 5 lakh would you multiply or divide divide divide what whatever you stored whatever you stored how do you recall that mrc press what equal to what is the answer 34 000. 744. please tell me the answer everyone online students yes is it 34514.74 have you understood the calculation should i explain again please do let me know once again okay listen arun wishes to uh buy a machine after 10 years right after 10 years that means in the future what is its cost 5 lakh so obviously this is what future value if the rate of interest for his investment is eight percent that means 0.08 find how much he has to invest every year that means a is what you need to calculate invest every year means it's a fixed amount regularly you have to pay so it's an annuity now fv of a r or a d a r why they haven't specified by default it is annuity regular what is the formula for fe of a r a into e r i e r i means what 1 plus i whole power n minus 1 divided by i i is 0.08 okay what is the first thing that you have to type 1 plus i what is 1 plus i 1.08 raise the power to how much 10 that means counter number should be 11. then what minus 1 please do it fast guys then press the divide by button i what is i 0.08 do you know a value that is what you need to calculate so what you do with this value store it in the memory by pressing what m plus where will this value go where will this value go to the denominator of lhs let's say how much what is fv of ar 5 lakhs all right 5x then divide by what ymrc this value has to be divided where it is in the memory how do you recall mrc press word equal to how much is the answer 0.74 guys this you need not right this is why you're understanding i'm writing is it required to write no you understood everyone is it clear is it clear everyone guys please tell me yes now let's move on to next problem current wants to accumulate rupees 20 lakhs to put purchase a plot at the end of 12 years he wants to purchase a plot at the end of 12 years so what is 20 lakh future value 12 lakh is future value uh how much he has to invest every year so what is that we need to calculate a so regular audio regular why how do you say regular not mentioned so fv of ar by default right correct so what is it a into 1 plus i whole power n minus 1 divided by i let's guys if you have understood the previous calculation you should be able to do this tell me what is it 82 873.61 is the answer is it please do it fast and tell me the answer clear everyone yes shall we move on online students guys i'm waiting for you here you got the answer yes clear let's move on to applications of annuity as it's not a new concept okay concept is again future value present value future value present value only where and all you see annuity that is what you're going to see now okay practically where exactly annuity you'll see right so the first of the application is leasing okay please understand guys what do you understand with liz what do you know about leasing first of all you tell me ah so uh what you said was okay uh if i take a a house on a lease base lease base so i have to let's say a lump sum amount i'll give you let's say how much uh how much 10 lakhs okay 10 lakhs is a lease amount so agreement is made for two years or three years depending upon uh the two years three years max basically nowadays it's made for two years then they can renew it okay so two years after two years what will happen if you want to vacate house whatever you you you are given initially that will be paid back to you given back to you right right so is it leasing what you have thought is it is leasing right that is actually not leasing no interest is not given back please understand leasing basically renting leasing basically means rent so please understand guys there is a rent actually uh involved here in what way even though it's a le it looks like what you're given a lump sum amount in the beginning there is a rent involved here guys let's say the person who takes it who takes this money the owner let's say he invest this at 12 per annum how much interest he gets per month one percent what is one percent on 10 lakh two zeros removed ten thousand so your rent is how much ten thousand your rent is how much 10 000. so basically i understand leasing is renting what is rent fixed amount paid regularly for specified number of periods leasing basically means what renting where fixed amount is paid regularly for specified number of periods is it clear is it clear okay so what is leasing actually means renting guys i'll give you one example okay practical scenario so that it will help you out to understand whether to go for leasing sometimes if you have an option between what if you want to choose an option between purchasing or going for a rent so which one to pick which one not to pick okay i'll give you one example please concentrate here okay let's say you have a manufacturing company okay you have a manufacturing company once manufacturing it could be a toy manufacturing company or any uh any company for that matter it's a manufacturing company what do you need for manufacturing company machines let's say you want a machine okay now you don't have a machine you want to purchase a machine you need to you need machine whether you purchase or you get it something somewhere else on rental basis you don't know but the main thing is that you need a machine okay for that there are two options there are two options the first option is purchase at let's say file x purchase at filex or lease lease means what rent at a rent um yearly rental of 1 lakh 25 000 for 5 years 1 lakh 25 000 for 5 years yes normally what do you think what do you think if i go for a rent i'll be paying one lakh 25 000 for 5 years how much i'll be paying 6 lakh 25 000. instead of that if i purchase i'll get it for 5 lakhs only and not just that i can use it for more than five years also that's how you think right that's how you think but can you compare wait wait but can you compare six lakh twenty five thousand when by when you will pay six lakh twenty five thousand tell me by the end of five years are you paying six like twenty five thousand in a single stretch are you paying six lakh twenty thousand today only no right each one lakh twenty five thousand you're paying at the end of first year then you know second year at the end of third year and so on this is the way you are going to pay and 6 lakh 25 000 how your thinking was is what 1 lakh 25 000 every year into 5 6 lakh 25 000 by the end of five years yes you will pay six lakh 25 000 by the end of five years but is that six lakh twenty five thousand what you pay for five yes comparable with today's file act is it comparable with today's file act never you cannot compare today's value with the future value you cannot compare today's value with the future value there is no comparison between future value and a present value that is one point understood there's one more point you may be thinking what after five years also i can use the machine please understand if they specify rent period is five years that means to say the life of the machine is only five years you have to understand whatever the rent period they will specify in the problems that itself is the life of the machine that means after that what will happen it will become a scrap clear okay now how to take a call whether to purchase this or go for a lease what is this one lakh 25 000 rent fixed amount paid regularly is it annuity regular or is it annuity due uh-huh how do you say rent is annuity regular after one year or one month only you pay the first trend right end of the period only you pay the first trend glazing means what renting right so it is annuity regular 1 lakh 25 is a value right a value and 5 years and normally in the leasing problem they'll specify the interest the borrowing cost they'll specify borrowing cost at say 10 percent per annum what do you mean by borrowing cost of 10 per annum please understand this how much rent you have to pay every year 1 lakh 25 000 borrowing cost basically means let's say when you're paying 1 lakh 25 000 suppose if you don't have money to pay obviously you have to borrow right borrow from somewhere and give it if you borrow it from someone they will not give it just like that right you have to pay the interest so what is the interest for your for the money that you borrowed 10 per annum understood understood now what you should do is this is annuity correct annuity 1 lakh 25000 is annuity find present value of this or future value of this hey what is this 5 lakh present value of future value purchasing cost when you want the machine today right it's a present value so this is the annuity case right would you find present value of this or future value of this if you want to compare future value present value would you compare with present value only or with future value you would compare it should be present value only right so this annuity you should convert that into what present value so what is pv of ar guys annuity regular a into 1 plus i whole power n minus 1 divided by i into 1 plus i whole power n what is i guys here 10 point one type it in the calculator one plus i means one point one how many years five years guys be very careful it's a present value there's a one plus a whole power n there's a one plus i whole power in denominator also after you get one plus i whole power and what do you do store it why because one plus i hold par and again it is required for the denominator right have you stored it one point one raise the power to five then store it by pressing what m plus then what you do continue minus 1 then what do you do divide what i i is how much 0.1 then what you do multiply or divide divide what mrc then equal to then equal to then into what a what is a here in this problem one lakh 25 000. so how much is pv of er 4 lakhs 73 000 848 whatever you see present value of this annuity even if you go on a rental basis the effective present value of this annuity is how much 4 lakh 73 843 whereas if you go for a purchase literally you are paying how much 5 lakhs so which one is better leasing is better or purchasing is better if the leasing cost is less than purchasing cost leasing is still a better one understood understood see it's not like one lakh twenty five thousand you're paying every year for five years you are paying six lakh twenty five thousand so if i purchase it will be five lakhs one lakh twenty five thousand extra it is that does not the right way of taking a decision when are you paying a 6 lakh 25 000 by the end of 5 years you're paying 6 lakh 25 000 so you must have a present value only to compare with the present value what is this 5 lakh purchasing cost present value what is this 1 lakh 25 annuity so you need to find the present value of this annuity then only the comparison happens so which one is better leasing is better you understood so when do you prefer leasing when the present value of leasing is less than purchasing cost you prefer leasing if the present value of leasing is greater than purchasing cost then purchasing is better when both are equal it is left to you if you want to purchase purchase it you want to go for lease purchase i mean go for lease because both are equally good have you understood the concept of leasing so in leasing problem what you'll be finding future value present value present present value because purchasing cost is always present value guys understood concept is clear concept is clear everyone yes yes yes okay so let us see see if you are if you have to make a decision between purchasing a machine or taking a machine on a leasing basis what you have to see find the present value of leasing annuity that is leasing means annuity rule right find the present value of leasing then we compare then we need to compare their present value if you want to come see if you want to take the decision between purchasing and leasing you have to compare their what present values always purchasing cost will be present value so find pv of leasing then compare with purchasing cost if pv of leasing is lesser than purchasing which one is better leasing is better if pv of leasing is greater than purchasing cost purchasing is better if both are equal equally good it's your wish so why don't we compare the future what is the future value of 5 lakh if the cost of money is 10 10 so what is p uh future value pv pv into 1 plus i whole power n so 1.1 raise the power to 5 1.1 razer power to 5 done into uh pv what is pv 5 lakh so what is fv of this purchasing cost 8 lakh 5 000 250 so now since the purchasing cost has become a future value you have to find a fv of ar now fv of leasing you have to find out fe of leasing will be what regular only a into 1 plus i whole power n minus 1 divided by i what is 1 plus i 1.1 raise the power to 5. do it minus 1 divided by 0.1 into a what is a 1 lakh 25 000 that example how much so even if you compare future values only leasing cost is lesser than but which one takes more time the present value takes lesser time future value because filak already it's a present value why do you waste your time in converting into future value so both the cases if you convert into future values also you get the same answer answer in the sense not this the decision which one is better which one is not which one is not to be taken that which one is not to be done in the sense purchasing or leasing so you can take a call on comparing the future value or you can take a call on comparing the present values also understood but better you take it take a call on comparing the present value because purchasing cost always given as pv only why do you again convert that into future value then find the future value of it two steps extra right guys understood so now so whatever i discussed so far the same points pv of leasing if it is less than pv of purchasing then the leasing is preferred that is better if pv of leasing is greater than pv of purchasing then it is purchasing is better okay if pv of leasing is equal to pv of purchasing both are equally good so it is left to the individual is it clear guys so far is it clear now guys uh we'll see in the point of view of lesser and lessee who is lessee and who is lesser less he means the person who takes it for lease kind of employee employer employee the person who works given an employment employer who has given a giver who gives a employment kind of employee employer only lease lesser is the person who takes it for lease lesser is the person who gives it for lease now tell me if leasing is better it is profitable for whom yes let's see so profitable for or whom let's see okay if purchasing is preferred then it is profitable for lesser profitable for lesser you can say here not for both both are equally good so it's neither profitable for lesser nor for let's see understood so in in in in terms of lesser lessee point of view if you want to see if pv of leasing is lesser than purchasing it is profitable for lessee if pv of leasing is greater than pv of purchasing it is profit profitable for lesser both are equal not for both is it clear everyone online students please do let me know is it clear your owner is lesser very good please we'll move on now let's see how you take a call now whether to purchase or go for a lease a machine can be obtained either by purchasing at 75 000 what is it pv off purchasing or losing purchase pv of purchase is 75 000 now what is this 22 000 rental means fixed amount what is it annuity a four years is n rate of interest is 11 means 0.11 find the weather find whether the machine can be purchased or not yeah guys what do you do should it be purchased should it be purchased no noise you can't take a call you have to work out so pv of purchase is 75 000 what do you do pv of leasing guys leasing is regular or due come on regular ar what is pv of ar formula a into 1 plus i whole power n minus 1 divided by only i or 1 plus i whole power and also will be there 1 plus i whole power n is also there okay now what is one plus i you would type one point one one all right raise the power to how much four would you continue calculation just like that or you store that value why because you need it for denominator after one plus a whole power n please store it by pressing what m plus then what you do minus 1 then what do you do divided by i what is i 0.11 then divide what 1 plus i whole power n where it is memory how do you recall mrc press equal to press equal to then into a what is a 22 000 so what is pv of leasing 68 253 guys leasing is better so leasing is better means should be purchased should the machine be purchased no pv of leasing less than pv of purchase therefore therefore leasing is better that implies machine should not be purchased you understood this is for your understanding i'm writing you need not write all this right is it clear everyone is it clear everyone yes thank god i'm getting responses very happy now thank you thank you thank you shall we move on what is 8 lakh pv off purchasing amount pv of purchase what is 1 lakh 1 lakh is the annuity what is n what is i okay pv of purchase we know eight lakh pv of leasing you find out let's tell me how much is pv i'm lazy only that much huh seven years you raised uh or five years seven years seven years only sure check once you are current just ask you to check what is the answer 75. leasing is better or purchasing is better i mean huge difference right eight lag you have to fight you have to pay by for purchasing if you go for leasing you'll be literally paying homage four lakh fifty six thousand three seventy five half almost half of it right lesser and let's see let's see leasing is better means if pleasing is better whom it is favorable guys leasing is better means if leasing is better it is favorable for for let's see let's see problem is like a lassi no if you like it it's a la seeds okay understood shall we move on okay shall we move on everyone understood guys please tell me clear yes or no yes we'll move on okay okay investment decision next application of annuity investment decision okay okay right guys don't read that sentence forget about that use this sentence it is okay if you understand the concept that is actually useless okay then it makes sense now if you read it doesn't make any sense nonsense it is understand the concept first then you read it then it makes sense listen once again i'll go back to the same example of machine in the previous uh case for leasing what i did what i said uh whether to purchase or whether to go for a rent or lease okay here also you purchase a machine let's say okay why do you purchase a machine why did you purchase a machine for manufacturing what do you want to manufacture you want to earn right you want to earn that's the main thing right you want to make a business out of it right okay so let's say you bought a machine by paying five lakh all right how much by lag five lakh now why do you buy your machine to put in a service so that manufacturing happens so that you can sell the product so that you get the income out of it clear okay let's say the machine gives you contributes rupees one lakh thirty thousand every year contribution how much contribution is one lakh thirty thousand every year for next five years this five years should be assumed as what life of the machine all right should be assumed as life of the machine if the rate of interest is 12 percent per annum 12 percent per annum okay this is the thing now what do you understand by machine contributing routine rupees 1 lakh 30 000 will it print money it will not print money right machine contributing 1 lakh 30 000 every year means you purchase the machine you put the machine into service the machine is going to do manufacturing so you get the what product you sell it and you get you make a income of 1 lakh 30 000 every year that is what is contribution by the machine so please understand contribution means it is not leasing problem it is investment decision problem i'll tell you what is investment decision how to take investment decision okay machine is contributing how much do you one lakh thirty thousand for how many years five years so what do you think how are common people things one last ninety five thirty thousand every year for five years six lakh fifty thousand so i'm making a profit of one lakh fifty thousand so he's a fool if he thinks that way right is he getting six lakh fifty thousand today only no but home this five lakh is being is paid when today only so there's no comparison for that six lakh fifty thousand and today's file correct so what do you need to do this is an annuity and you may be thinking where why this 12 percent a leasing problem it's it was a borrowing cost to pay the lease if you don't to pay the rent if you don't have money you borrow it from someone and you pay the interest all right but here in contribution where the interest rate from where did the interest come from what is it any can anyone can tell i'm talking about this this part i'm not talking about this file i'm not touching upon this file act no is it a borrowing cost 12 person what is this rate of interest is 12 percent per annum what do you understand by that machine is contributing one language doesn't every year what are you doing with that money you invest at twelve percent per annum that's what the meaning of it see when you want to pay the rent you want money to to be given as a rent when you're investing money machine is contributing you money what do you do with the money will you keep it just like that no you'll have to invest right right so that is what is rate of interest for your investment one lakh 3000 when you get the receive the money you'll invest that at 12 per annum understood is it clear now guys once again as you did in case of present well i mean uh leasing problem you compared the present value this five lakh is the present value yes or no when do you purchase a machine today only so this this annuity this annuity what do you do find the present value of this annuity pv of annuity regular audio guys yes array that means to say that you purchase a machine you put the machine into service the machine will give you one lakh rather than today itself no right if it gives online criticism today itself it means to say it is annuity you is it annuity it is annuity regular so tell me now a into 1 plus i whole power n minus 1 divided by i into 1 plus i whole power and what is it tell me tell me what is it value why not tell me uh whatever value four lakh sixty eight six twenty now guys you invested how much by lack but literally how much you're getting should you do this investment you invested five lakh you're getting great in returns how much four lakh eight sixty eight thousand six twenty is it a good investment what is this investment called as can i say guys listen first can i say whatever i invest it goes out of me that is cash outflow can i say this investment as cash outflow and guys returns will come to me inflow this is cash inflow tell me guys for a investment to be a good investment inflow should be less than outflow or more than outflow more than or at least equal to if it is at least equal you're getting the compensation for your money yes or no even if it is equal at least you're getting the compensation for your money if not the profit if it is greater yes it's a profit if it is even equal also it's a good investment only because you're getting the compensation for your money have you understood inflow means what whatever comes back to you in return that is in flow what is outflow whatever you invested how much you invested here five lakh that is cash outflow so what is that you got in written in terms of present value four lakh sixty eight thousand six twenty that is in flow so inflow is lesser than outflow is it a good investment it's a loss so should the machine be purchased yes no machine should not be purchased you understood so that's what now it makes sense to read the sentence what is it if pv of cash inflow is greater than or equal to inflow means what returns pv of cash outflow what is outflow investment invested amount then the investment is said to be good otherwise otherwise means what less it is a does it make sense now to read this everyone guys you understood everyone please tell me understood don't tell me i did not get the calculation we have done enough of calculations so by now you should be thorough with the calculations now still if you have please ask me no issues for today yeah understood everyone okay shall we solve problems now i already solved one problem now for you understand me guys you understood the meaning of inflow and outflow what is inflow returns outflow investment so for investment decision problems also you need future value present value present value policing problem present value for investmentation problem present value for sinking fund future value please keep it in mind next net present value is what you mean by net present value effective present value see how many present values you have in investment decision cash inflow pv of cash inflow and pv of cash outflow so net present value means pv of cash inflow minus pv of cash outflow guys this npv basically gives you what how much is a profit for you or how much is a loss for you yes or no this npv basically tells you how much is a profit for you or how much is a loss for you now tell me when do you get a profit inflow more or inflow less inflow more it's a loss i mean profit if inflow is less it's a loss understood now based on npv also you can say whether it's a good investment or a bad investment if npv is greater than or equal to zero tell me it's a good investment or a bad investment when npv is greater than or equal to zero if inflow is more or equal to outflow then only npv is greater than or equal to zero so is it a good investment good investment if npv is less than zero that means negative when when inflow is lesser than outflow so therefore it is loss understood with respect to npv you can say whether the investment is good or loss or bad all right that's understood understood so what is npv pv of cash inflow minus pv of cash outflow repeat npv again sir okay listen sir what is npv net present value it is the difference between the inflow and outflow both inflow and outflow must be expressed in present value because it is npv net present value so npv is pv of cash inflow minus pv of cash outflow tell me when is npv more than or equal to 0 more than 0 tell me positive value tell me this first term should be more than the second term if the first term is lesser than the second term will it be negative or positive negative if it is negative it is loss if it is positive or equal at least it's a good investment positive means profit equal means it's a good one fair enough understood everyone yeah an investment is said to be good if npv is greater than or equal to 0 it is a loss otherwise once again otherwise it's a loss guys is that clear everyone clear so far shall we move on now i expect you to do the calculation what is this 80 000 given purchasing the purchasing means investment or returns investment is called as out floor inflow so this is pv of outflow cash outflow cash outflow now what you need to find pv of cash inflow pv of cash inflow let's tell me for inflow regular audio it ar is is the formula for pv of a r a into 1 plus i whole power n minus 1 divided by i into 1 plus i whole parent guys by now you got used to the formulas now sixty thousand seven forty six okay fine so what did you understand inflow is less or more so is a good investment or a bad investment it's a bad it's a loss correct it's a loss utter loss yeah pv of cash inflow cash inflow less than pv of cash outflow therefore it's a array therefore it is a loss is that clear everyone hurry what is a 20 000 do the calculation once ah guys what is pv of cash inflow you got pv of cash inflow huh 72 000 who told me this 60 000 guys i should not trust you now how much seventy two thousand ninety five okay uh so is it a good investment still it's a loss right because because it's lesser than invested amount which is 80 000. so it's a loss right understood clear everyone is it clear seventy two thousand ninety five guys i wanted to ask you one thing so tomorrow we will have a session we'll finish off this chapter all aspects in the sense previous paper questions also is it fine we'll have it on monday so i'll give you a questions question papers so in this in this uh ppt only there will be previous paper questions there's nothing like tough so before you solve papers okay what you need to do go through all the concepts so tomorrow you prepare everything tomorrow you sit prepare simple interest all shortcuts types second compound interest concepts only four types are there then annuity prepare on that tomorrow only for preparation day after take the previous papers all right there are a few more papers i mean i have given three papers here few more papers i will share by tomorrow day after you will get the papers okay you'll get the papers please complete solving all the papers you should be able to solve all the questions i i bet you should be able to solve 90 percent of the questions comfortably any doubt you mark it and ask me in the next class so that next class we can start with a new chapter so i'll give you uh whatever time that you i mean i want you to do uh solve the questions you have to put in your sincere efforts okay so then only you can practice and you can be what how you can have a clarity on the chapter if everything i only give so i thought of actually doing it for tomorrow solving all papers but since you want uh off okay you can prepare to for tomorrow the whole day you can prepare on this chapter day after make sure you complete all the papers if you do that 12 to 16 marks will be in your pocket and underline the questions wherever you are having doubt those questions i will solve in the class so by monday we'll start with a new chapter maybe one hour i will discuss with whatever doubts you people have is that fine is that fine everyone okay i'm not okay okay okay guys let's whatever yeah uh look at this question can you solve this as an assignment what you want to do should i give it as an assignment question same pv of cash inflow pv of cash outflow i'll just write assignment yeah i'll just put assignment yes you have to tell me which one is preferred tell me first of all what is pv of outflow cash outflow i'll just mark and give it to you okay pv of cash outflow all right and what is uh annuity 15 000 and what is this n and what is i 0.1 so find out pv of cash inflow and just decide which one is preferred yeah can you do that so i'll just leave it as an assignment question please solve it listen to the next concept that is valuation of bond oh already answered yes good investment is it a good investment huh better buddy [Music] already have sold it okay anyways see i just wanted to uh make sure that annuity problems are so fast you can do the questions very easily there's no types in annuity whatsoever you need to just decide regular due future value or present value that's all but whereas simple interests and components there are varieties right but annuity there is no varieties actually future value present value future value present value except that there's nothing actually right okay guys let us see next concept valuation of bond okay what is bond basically it's a bond is basically a debt security in which an issue issuer owes the holder adapt and is obliged to repay the principal and interest bonds are generally issued for a fixed term longer than one year oh my god nothing gets into the head right okay listen what's basically this means okay listen guys so you know uh indian government uh purchases oil from uh gulf countries right purchases oil even from russia also recently they have signed right okay let's say india purchases oil so guys sometimes it so happens that uh there won't be money to purchase let's say for 100 crores they're purchasing the crude oil okay so they won't be having money let's say so what they'll do they'll give the bond saying that i am obliged to pay 100 crores or maybe 500 crores whatever oil they purchase this 500 crores i'm blessed to pay this 500 crores they'll write it in a bond yeah bill of exchange and they say that this only not 500 grows along with that an interest along with so it's a security right whatever they're giving it giving it as a bond it's a security debt security debt security and they're obliged to pay with a little interest and normally this bond is issued for a period more than one year after one year the bond matures so whatever the amount is that is specified in the bond has to be paid understood so that is basically a boundless so bond is generally issued for a period of period more than one year so is it clear is it clear no guys for bond uh calculation not a james bond okay for bond calculation please understand uh the maturity value of a bond is always they'll specify par value of a bond please listen to me first of all par value of a bond let's say par value of a bond is 5 000 par value basically means maturity value par value basically means what maturity value so maturity when will the bond mature after the specified duration so is it the future value or present value par value is always future value so it will specify in the question if the power value of a bond is uh what in the question three thousand per value for bond is three thousand so what is this future value and what is the duration of this bond three years time is three years all right now what is the nominal rate eight percent per annum 0.08 and they have given one more rate of interest which is ten percent per annum please guys understand there is a note point that you need to understand okay always to find to find future value of interest future value of interest consider nominal rate of interest to find the future value of interest find out what nominal use what nominal rate of interest note number two for valuation one problems note number two to convert to convert fv into pv what do you mean by this future value into present value use rate of return given rate of return given in the question so there will be normally in the valuation of one problem there will be two rate of interest one is nominal rate and the other one is real rate of rate of return rate of return so is this clear these points are very very important to be understood why do we have to convert future value into present value because what they ask in evaluation of bond problems is if the power value is thousand all right what is three thousand maturity value of the bond when it matures after three years so after three years how much you'll get as a maturity value three thousand if the maturity value of the bond is three thousand at what price you need to purchase it today at what price you need to purchase it today that is what is called as present value of the bond all right so you will be finding what at what price the bond may be purchased means what you need to find pv of bond guys please understand pd of bond means it is future value of first year interest or let me write down pv of first year interest all present values only your take pv of first first year interest plus tv of second year interest how many years are there three years so pv of third year interest so all three years interest are considered now now we need to consider pv of this par value pv of per value so all values have to be converted into present values that will be the present value of bond is it clear is it the first step clear so all interest whatever you get that have to be converted into present value each first-year interest second-year interest third-year interest all of them have to be converted into present value guys why interest have to be converted into present value when do you get the interest at the end of first year the end of second year at the end of third year those values are what future values those values have to be converted into present values you understood then finally pv of power value par value means maturity value of the bond so this is what you should be doing to evaluate your bond is it clear now how do you find out pv it is fv divided by 1 plus i whole power n correct what is pv fv divided by 1 plus why am i using f3 tell me because you will be knowing only future value of interest you will not know present value of interest so first of all fv of divided by 1 plus i when do you get the first year interest at the end of first year so what is the power i have to use n value is only one for the second year interest fv divided by 1 plus i whole percent when do i get the second year interest at the end of 2 year that equal in today's value will be obviously i have to raise power 2 correct third year interest when do i get at the end of 3 years that equivalent present value if i want to find out i have to divide by what 1 plus i whole power 3. is it clear finally this is par value means basically future value future value of a bond divided by what 1 plus i whole power 3 is it clear is it clear everyone is this point here so all these fbs are what fv of interest fe of interest fe of interest but this is fv of par value of the bond now guys what does see to find out future value of interest i have specified the first point what is it what interest has to be considered nominal rate that nominal rate should be calculated on what the par value three thousand into eight percent how much it is 240. so i'll write the calculations over here so 240 is the interest that you get future value of the interest for one year divided by what for converting future value into present value which return you have which interest you have to consider so for this i what i should consider written that means 1 plus 0.1 understood how did we get 240 tell me par value into nominal rate nominal rate is 8 percent so that is how you get 240 guys tell me again fv of second year interest what is it again ten percent on what sorry eight percent on what three thousand which is 240 but when do you get that at the end of second year so it's gonna be one plus zero point one whole power two and third year interest again two forty rupees only divided by what one plus zero point one whole power three finally all three year interest is done finally what i do what i am going to do fv of bond that means power value of the bond which is 3 000 divided by 1 plus 0.1 whole power 3 correct nice this can be carried out in one step in the calculator how do you do it type 240 divided by zero point sorry 1.1 m plus m plus okay then type 240 divided by 1.1 press equal to how many times 2 times why because power 2 is there second term then what do you do after that m plus next 240 divided by 1.1 press equal to how many times three times then press what m plus all right next 240 sorry 3000 divided by 1.1 press equal to how many times three times how much ever is the power so much so many times you have to press equal to finally what mrc answer [Music] is it 596 this check once again what is it let's please do the calculation again exactly do it once again do it once again 240 divided by 1.1 m plus it is 2850.78 two eight five zero point seven eight that's the answer please do it once again guys 240 divided by 1.1 press what m plus 240 divided by 1.1 equal to how many times twice because whole power 2 is there m plus 240 divided by 1.1 whole power 3 it is there so press equal to thrice m plus 2850.78 is the right answer here everyone is it clear guys valuation of bond never been asked in the exam but even if they ask this is what you should do you should be doing which step this step you should be doing all that i have written is for your understanding all that i have written is for your understanding they have never asked so far but for you they may ask i can't guarantee that in the so far in the history of ca foundation or ca cpt this question never come okay so it may come so better be prepared so what how do you find the present value of the bond pv of first year interest plus p we have second year interest plus pv of third year interest plus pv of power value how do you find pv fv by 1 plus i whole power n fv of in first year interest divided by one plus i why only whole per one because first year second one uh fv of second year interest divided by one plus i whole power two plus fv of third year interest divided by one plus a whole power 3 plus f e of bar value divided by 1 plus a whole power 3. now for finding out fv of interest what is the first point i have specified consider nominal rate that is calculated on what power value so 3000 into eight percent so fv of first year interest is 240 the same will be second year interest the same will be third year interest what differs powers will differ finally if we fv of power value that means 3000 divided by 1 plus i whole power 3. so use m plus mrc calculations you can get the answer in one step in the so these points whatever note that i have given that has to be remembered by you don't write all these things in the exam clear guys is it clear so what mean m e k n in the calculator m e k n is there in the calculator yes i think you are using a scientific calculator it is not there yes one last concept i'll do it's a small concept with that we're almost done okay perpetuity what is it no sir when we get answer m e k alright don't worry about that m e k and all that is what it shows can you don't don't worry about that don't worry about that what you have to worry is the count what you have to worry is the counter number and the answer that's it okay don't worry about that okay guys let's move on perpetuity okay guys you know what is annuity what is annuity fixed amount paid regularly for specified number of periods perpetuity fixed amount paid regularly for indefinite number of periods what is the difference their number of periods how many periods it has to be is it for five years or is it for ten years we know it but perpetuity number of periods will not be known it is indefinite definite means you'll they'll specify how many periods where you come across perpetuity fixed amount paid regularly but number of periods are indefinite pension yeah see when earlier there was a pension idea of pension in the government organizations right once the person retires at the age of 60 or 58 he is entitled for pension so whatever is a salary during i mean at the time of his retirement the 50 percent of the i don't know how much percent exactly it is some percentage of his salary would be given as a pension until the person dies yeah obviously after a person dies there will be one nominee that's it nominee means normally his wife okay she'll get after she dies no no one will that will not be transferred if it transfers the government has to bear a lot of now the pension plan is not there actually only gratuity is there once you retire you get graduate epf and all pension is not that it's a huge burden for the government right it is our money only right the government is giving it's not giving by somewhere it's our money it's our tax money right okay anyways so what is perpetuity fixed amount paid regularly for indefinite see you will not know for how many years you'll get a pension right you'll not know is it for 10 years or 20 years or 30 years or 40 years you will not know right so why it's a fixed amount or receipt amount rather you can say paid regularly indefinitely how many periods we don't know okay so there are two types of perpetuity one is normal or ordinary perpetuity the other one is growing perpetuity so what is this normal perpetuity or a multi-period perpetuity basically guys what you'll be doing here is you'll be finding out present value of your perpetuity so what do you mean by present value of perpetuity is please understand let's say you get a pension of 5000 every month for next let's say for indefinite number of periods so that lump sum amount it's for in infinite number of periods right we don't know how many periods what would be its equivalent present value so is it an exact value definitely it's not going to be exact value it's an approximation only so if you receive 5000 5000 every month as a pension for indefinite number of periods what will be its equivalent present value that is what is pv of perpetuity this please understand this is not the exact value it's going to be an approximation and it is simply r divided by i so what is r basically r is receipt amount what is our receipt amount receipt amount means whatever the fixed amount that you receive every month as a pension as a perpetuity that is what is r you understood and i is rate of interest please understand one thing here r and i should be in same terms what i mean to say r and i should be in same terms normally i will be per annum right per annum sometimes receipt amount will be given per month you have to convert that into per annum because both it should be in terms of i mean same terms actually if you keep receipt amount per month and interest rate per annum the calculations will be wrong both should be per annum only so what do you do to get the reset amount per annum into 12 you do if you suppose if they give you per month receipt amount understood understood so that is what is normal perpetuity okay r by i r means fixed amount or fixed payment or receipt amount i is interest rate so there is one more perpetuity that is growing perpetuity in growing perpetuity please understand along with i growth rate is also given and will be given to the pension holder or perpetuity holder so how you do the calculation for pv is so it is r divided by i minus g see for normal perpetuity it will be just r by i for growing perpetuity instead in addition with i you will have minus g so that is growing perpetually so how do you how do you how do you identify normal perpetuity and a growing perpetuity in a normal perpetuity please understand only one rate of interest will be given in growing perpetuity growth rate is also given the moment you see growth rate along with nominal rate it will be growing perpetuity understood understood so perpetuity problems are very easy it's just r by i or r by i minus g that's it okay one problem will solve will wind up for the day okay guys find the present value of the perpetuity of rupees 6000 payable monthly at eight percent per annum tell me is it a normal perpetuity or a growing perpetual how do you say normal only one rate growth rate is not given so pv of perpetuity is r by i or r by i minus g r by i guys please understand receipt amount is given per month right so r is 6 000 per month how do you convert this per annum 6000 into 12 which is 72 000 per annum correct okay now substitute 72 000 in place of r what is i guys 8 that means 0.08 so present value of this perpetuity is understood understood so sometimes if they may give you growth rate also if they give you growth rate minus g you have to do and divide understood clear so i have left compound growth rate i'll do it in the next class i'll not do it don't worry okay so on this there's no question asked so after compound growth rate i have given you straight away previous paper question so ch here i'll be explaining the next class along with your doubts okay so yeah so i have given previous paper question three papers i have given each paper will have 12 to 14 questions okay please solve them before solving what you need to do tomorrow the whole day for preparation guys no need to prepare from icm material forget about icing material solve whatever i have given the concepts the shortcuts you see all right then solve previous paper questions there are around 35 40 questions so along with that i'll share few more two more papers solve that also consolidate your doubts and come for monday's session is it clear is it clear so it should get completed in all aspects yeah can you [Music] we'll complete the concept that is remaining only one concept remaining that is compound annual growth rate c a g r all right so let's see what exactly is cagr they say you're running a company okay let's say it is some eight years old okay in those eight years how your companies has progressed how your company has grown okay if you want to calculate over a period of eight years okay that is called as compound annual growth rate and you're not seeing from first year to second year how the growth is from second year to third year how the growth is and you're not seeing year by year rather for complete span of eight years what is the overall growth and that growth is called as what compound annual growth rate it is not year by year for a given period of time maybe eight years or maybe five years or four years or maybe six years for that period of time what is the growth of a particular business that is called as compound annual growth rate am i clear okay cagr is a term used to describe the growth over a period of time of some element of business for example it could be the revenue it could be the income etc right nice let us see the formula to calculate cagr how do we calculate a ca grs okay it might look complicated but actually while solving questions it is not that complicated first of all you must know what is each and everything that is vn v naught t n t naught and all guys this formula what what has been displayed here the first one it is a fractional value formula that so why there is no in 200 and look at the second one what's the difference the entire thing is multiplied with 100 to get a percentage value now let us look into each and every term that is there in the formula first one tn what is tn n stands for nth year or end period n stands for nth year or end period t stands for time or rather we call this end period or end time t naught 0 refers to the reference year or the beginning year we can take it as reference here or beginning period we n it's a value corresponding to the nth period or end period okay what is v naught it is a value corresponding to t naught so first of all what you need to identify to find out c h e r s the reference here that is beginning here and the end period that is t naught and t n then the whatever the value corresponding to t naught will be v naught whatever the value corresponding to t n will be v n okay and thereafter you can just put those terms in the formula to get the answer but the problem with c h e r s guys look at the power here what is it whole power 1 by t n minus t naught let's say suppose if t n minus t naught is equal to 3 okay please concentrate here suppose if t n minus t naught the difference between end period and the beginning period is 3 what do you understand by that whole power 1 by 3 right because t n and t naught t naught t n minus t naught is there in the denominator look at the power it becomes what whole power one by three tell me what is the meaning of whole power one by three cube root whole power one by two is square root whole power one by three is a cube root can you find out a cube root in a simple calculator is there a provision to find a cube root there's a provision only to find a square root there's only a square root button in your calculator there is no cube root button so you're not allowed to use a scientific calculator so the problem with the roots other than the square root if it is cube root fourth root you can find out i told you how how fourth root suppose if it is whole power one by four you can always put this as 1 by 2 into 1 by 2 press square root how many times 2 times for 4th root you can press the square root 2 times you get 4th root but cube root it is not possible in small amount of time so what to do for that so you are not going to use this conventional formula because here the villain is what who is the villain whole power tn minus t naught let us kill this villain shall we kill him who's the villain here in the formula 1 by tn minus t naught so let us eliminate that fellow right so let's see how we do it guys you understood why we are thinking of eliminating 1 by t n minus t naught because if you come across the differences t n minus t naught is 3 whole power 1 by 3 is a cube root you can't find out a cube root or fifth root or 6th root or seventh root in your simple calculators so what you can do is you can modify the formula so modified formula for cagr guys the problem creator here is whole power one by t n minus a t naught so we need to eliminate this before i eliminate this so i'm not going to take a percentage formula i'm going to take a fractional value formula guys this minus 1 can be sent on the other side become what plus 1 so i can write 1 plus c a gr on the left hand side can i do that minus 1 becomes a plus 1 and what is remaining on the right side we n by v naught whole power what 1 by t n minus t naught so still we haven't cleared this 1 by t n minus t naught so how to eliminate that raise the power with t n minus t naught guys what happens if i raise the power to t n minus t naught on both the sides 1 plus c a gr will have a power t n minus t naught what happens to v n by v naught the power gets eliminated yes or no because one by t n minus t naught is there in the power already if you raise the power power get multiplied right so t n minus t naught so powers get eliminated so why we raise the power both sides with water t n minus t naught is that clear is that clear now so this is the modified formula for c a g r so you understood how we got this modified formula what you should be doing is what you should be doing is only apply this modified formula so one plus c a g r is equal to v n by v naught which which term will have a power tell me finalize formula nhs or rhs lhs will have a power what is the power of lhs tn minus t naught so this is the formula you should be using but unfortunately the question what is asked will be what to find ca gr if you don't know what is ch or how do you raise a power right you will be asked the question to find c h e r but you don't know what is c h here without knowing uh c h here how do you add that with 1 how do you raise the power to t n minus t naught you're understanding what i'm asking itself is the question asked right what do you do cagr will be there in the options right cagr will be there in the option just plug in the cagr in the calculator straight away you can do it now tell me guys this ca r is a percentage value or a fractional value why how do you justify that because the formula which we took was the first one not the second one right it's a fractional value guys you understand what is fractional value if i give you 35 percent what is the fractional value of 35 percent zero point will there be a zero after a point for two digit number no after a point just the number as it is tell me what is eight point five two percent means zero point two eight five two it's a two digit number right twenty eight point five two so after a point there is no zero suppose if it is two point eight five percent after a point there will be a 0 followed by the number 285 hope you understood don't use calculator for converting percentage into decimals is it clear everyone online students guys is that clear everyone please do let me know is that clear yes so shall we move on to soul equations on ca yes yeah so you will not be using this formula which formula the conventional formula rather you will be using this so what is the first thing that you will do identify t naught t n v naught then v n then write down what is v n by v naught on one side right that is rhs v n by v naught write down that value then what you need to do plug in the options one plus that option raise the power to t n minus t naught take the difference between t n and t naught that is t n minus t naught then raise the power to that number you know how to raise the power of a value type a value press into keep pressing equal until the counter number is one more than actual power if the power is four the counter number should be 5. and some calculator you may have to press into twice dikshitar i think you remember it i remember that because i explained it to you the last class right all right shall we have questions on those everyone okay guys look at the question find c a g r okay guys have this specified uh the reference here here in the question they haven't specified the reference here if they don't specify any reference here the first tier itself is taken as t naught and the last year is taken as t n so what is the value corresponding to tn vn tnt and i'm talking about tn what is the value corresponding to tn vn which is 400 this is vn what is the value corresponding to t naught 200 is v naught guys what's the formula that you will be using tell me to find c h here one plus c a g r whole power t n minus t naught should be equal to what v n by v naught let's divide v n by v naught tell me the value 2 right 400 by 200 is 2. write down that value on the paper right now what you need to do is take the first option guys eight point nine two percent in fraction what is it zero point zero eight nine two when you add one to it do you use a calculator to add one to it no one point zero eight nine two the result of one plus c a g r is one point zero eight nine two type that and first of all tell me what is sorry this is t n right i'm sorry yeah tell me guys what is t n minus t naught t n minus t naught how much it is four right because t n is 2017 t naught is 2013 so it is four now what do you do point zero eight nine two raise the power to four you know how to raise the power to four press into keep pressing equal until the counter number is five so do you get that value one point so that is not the right answer right what do you do guys while choosing the options i told you how how smartly you can choose the options what did i say moderate value amongst the given option which is the moderate option option b is actually so please don't check with the least option always always check with the moderate option so 18.92 means 0.1892 when you add 1 to it it is 1.1892 are you getting this 18.1 18.92 percent means 0.18 because 2-digit number 18 means 2-digit number after the decimal point there won't be 0 as it is one eight nine two zero point one eight nine two when you add one to it it will become what one point one eight nine two please type that value in the calculator one point nine nine nine nine that means approximately it is two one point one eight nine two press into keep pressing equal until the counter number is what power should be what four right t n minus t naught is four so counter number should be five so are you getting it so which is the right answer eighteen point nine two so i'll just write down like this option b eighteen point nine two percent means zero point one eight nine two and one plus c here will become what one point one eight nine two whole power what is t n minus t naught 4 it is 1.9999 equal to 1.9999 which is approximately equal to 2. therefore option b is the answer have you understood you need not write this it's only for your understanding clear everyone sure sure sure i'll do that once again yeah have a look first of all you identify which is t naught and which is t n what is t naught they have they haven't specified which is reference here if they don't specify the first year itself is t naught so i have marked 2013 as t naught the last year is t n so 2017 is t n the value corresponding to t n will be vn that is 400 the value corresponding to t naught will be v naught which is 200 so what is the first thing you will write down the formula the modified formula of cagr so we n by v naught what is vn 400 divided by v naught is 200 what's 400 by 202 so you'll write down that value on the right hand side now always plug in the moderate option don't plug in the least options or the highest option that's a smart smart way of plugging in the options which is the which one looks the moderate option what do you understand by moderate there should be a value more than it there should be a value less than that that is called as a moderate value that is how you identify the moderate value so if you use option b as one of the options that you are plugging in okay so 18.92 percent is it a fractional value no it has to be converted into a fractional so it will become what 0.1892 when you add 1 to it don't use calculator to add why do you have to add one to it because it is one plus ca gr so point one eight nine two when added with one it will become what one point one eight nine two please type that in the calculator one point 1.1892 raise the power to t n minus t naught so t n minus t naught t n is 2017 t naught is 2003 sorry 13 the result will be how much 4. now please raise the power to 4 press into keep pressing equal until the counter number is 5. so how much are you getting 1.9999 which is approximately equal to the desired number which is 2 isn't it vinai you understood now yes okay shall we have one more question on cagr okay find ch here for this the options are right here okay so which option do you pick first of all moderate 23.62 or 18.62 javish which option would you pick guys before that please mark t and t naught v and v naught which is tn 2000 22 is tn which is vn option here vn is how much 100 v naught is 60 tn is 2018. so what is tn minus t naught is 2022 minus 2018 which is so t n minus t naught is equal to how much four so what's that modified formula one plus c a g r whole power t n minus t naught should be equal to what v n v n by v naught tell me what is v n by v naught you got 1.6666 all right so now which option did you check first of all option b you checked so for option b you got more or less more so obviously you have to go for the option which is less than that there's only one option which is less than that right for 18.62 percent it is point one eight six two when you add one to it will become one point one eight six two raise the power to what four how much do you get is it one point six six or more than that it is more than that so if it is more than that you have to go for the lesser option there's only one option which is less than 18.62 that is 13.62 so option a if you plug in option a so what is the answer you will get one three six two will be one plus c h r guys you understood one point one three how we got one point one three six two by adding one plus c h r because c here is point one three six two when you add one to it it'll become one point one three six two whole power what four tell me the result of it six six six five so that is equal to the required value only right approximately therefore option a is the right answer have you all understood everyone is it clear clear sure online students shall we move on okay shall we move on this is already this has been discussed right nominal rate of interest so what is nominal rate of interest it is the interest that is guaranteed for your investment it is the interest that is guaranteed for your investment or even if you take a loan it is an interest that you have to bear right it's a borrowing cost so nominal rate of interest is basically the interest for your investment all right so it will have how many parts what are the two parts of nominal rate real rate and inflation rate so which rate tells you about how much is compensation inflation rate which which part of nominal rate tells you about how much is profit real rate all right so it is stated interest for any investment it is an interest that is guaranteed for your investment it is a stated interest for any investment guys already i discussed about this but still if a certain amount is invested at 10 percent per annum for a cert certain number of certain number of years then the nominal rate of interest is said to be 10 percent whatever the interest that is guaranteed for your investment whatever they mention as a interest that is always what nominal rate of interest all right this normal rate of return has two parts what are the two parts real rate and inflation rate real rate of return and inflation rate so we can say nominal rate of return is equal to real rate of written plus inflation rate already we had discussed this isn't it but take it as a formula nominal rate of interest is real rate of written plus inflation rate so tell me suppose for the same nominal rate of 10 percent if the inflation rate is 7 percent what will be the real rate 3 percent this point was discussed earlier right but i had not given as a note so previous paper questions on time value of money right so let's take one by one and let's see how fast we can do the questions right so first paper is 2019 june okay these questions are from 2019 june look at the first question a sum was invested for three years as per ci and the rate of interest for the first year is nine percent second year it is six percent and third year is three percent per annum respectively remember this is as per what ci rate of interest are different for different time duration find the sum if the amount in three years is 550 rupees they have given off the amount what is that they're asking principle guys what is the formula that connects amount in the principle p into 1 plus i 1 into 1 plus i 2 into 1 plus i 3 so what is that a is equal to p into 1 plus i 1 into 1 plus i 2 into 1 plus i 3 guys only this much you can write down on paper ok please understand what is that you need to find out p right only p will remain on the right hand side every other term will go to the left side and gets divided yes or no 1 plus i 1 will get divided 1 plus i 2 also will get divided 1 plus i 3 also will get divided all right look at the rate of interest they're all percentage values but you have to convert them into fractional values okay so what do you know out of a and p we know a type a what is a given 550 divided by what 1 plus i1 what is 1 plus i1 1.09 1.09 again divided by what 1 plus i2 what is 1 plus i2 one point 1.06 again divided by what 1 plus i3 what is it 1.03 so what is p 462.16 so option c option c is the right answer you understood you understood guys they have not asked you to find the amount they have asked you to find the principle by giving off amount is that clear what we did here everyone okay look at the next question they have given p i square p into i square they have given 96 and the rate of interest is eight percent what is p nice p i square what is it equal to 96 guys don't you think high-end r are one and the same i and r i is rate of interest even r is also rate of interest guys what is that we need to find tell me p so what happens p is equal to 96 by i square what is i eight percent means 0.08 the whole square guys you know how to divide this type 96 divided by 0.08 press equal to how many times 2 times because whole square is there you have to press equal to only 2 times 96 divided by 0.08 press equal to how many times 2 times only once if it is only 0.08 since it is 0.08 the whole square you have to press equal to how many times twice by pressing equal to twice it means to say that you are dividing it by 0.08 how many times two times so how much is the answer 15 000 option b you understood it's a laddu question pi square is given off you need to find p even i is also given off we need to find only p p is equal to what 96 divided by i square that's it okay now look at the next question that is also laddu principle is how much principle is 5000 rate of interest is 15 percent t is four and a half i is equal to ptr then i will be how much there's no hundred actually three thousand three seventy five what is that guys p t r percentage p is how much five thousand type it t is how much four point five into r is how much 15 press a percentage isn't it 3375 it does next question guys which type it is a sum of money amounts to 6200 in two years and seven thousand four hundred and three years as per si then the principle is which type type two amounts in terms of type five what's the shortcut to find the principle a two minus a one divided by t2 minus t1 into t1 minus a1 suppose if i multiply t2 then i have to subtract a2 that's it no so do we have to find sr8 per annum here no only the principle take your calculator which is a2 which is a2 guys 7400 minus a1 is 6200 pressure divided by button t2 minus t1 don't use calculator for t2 minus t1 t2 is how much 3 t 1 is 2 3 minus 2 is 1 straight away into what t 1 t 1 is how much 2 minus a 1 is 6 200 so what is it 3 800 option c tell me guys any question will it take more than 30 seconds no question will take more than 30 seconds i think most of the question you solved within 5 10 seconds right so for reading the question it will take hardly 10 seconds then for solving 10 20 seconds that's it within 30 seconds you should be able to solve the question is it clear everyone guys is it clear this is type 5 off should i write that type 5 of simple interest you land identified right okay shall we move on okay the effective rate of interest does not depend upon amount of principle so it is evident in the formula itself what is eri 1 plus i whole power n minus 1 there is no principle here in the formula right if i have a principle along with this that is the formula for what ci ci from ci formula only we get effective rate of interest right up which if you exclude p from it it is eri so it doesn't depend upon what principle there's no principle in the formula and i proved it also right for the same rate of interest i gave you two principles and i proved that whatever may be the principle effective rate of interest doesn't get affected hope you remember that i gave a principle as 10 000 and i change the principle as 20 20 000 so effective rate of interest doesn't depend upon the principle right okay next question guys the simple interest if the principal is 2000 and the rate of interest and the time are the roots of the equation x square minus 11x plus 30 equal to zero guys they have said what time and the rate of interest are the roots of this quadratic equation there is you've learned a bit of quadratic equation in your schools yeah we have to split the middle term by mult first of all multiply the first and last terms it is 30 x square tell me the two factors for 30 x square so that by adding the two you get minus 11x 6 and 5 minus or positive minus six and minus five guys don't plug in those values and solve for x okay these are what factors roots will be exactly of the opposite sign minus 6 and minus 5 are factors don't solve it in a conventional normally how do you solve it in conventional method x square minus 5x minus 6x plus 30 then combine first two and last two terms take common term x by the time you complete doing that exam will get over please don't let do like that okay so please understand whatever the fact is understand roots will be exactly of opposite signs all right especially when you have coefficient of x square is 1 if the coefficient of x square is other than 1 then you have to do it conventionally okay remember the coefficient of x square in the given quadratic equation is 1 whatever are the factors roots will be exactly of opposite side so tell me what are roots 6 and 5 6 and 5 are the roots so they are what t and r values yes or no so which is t which is r it is not required to you y what is the question asked simple interest what is simple interest guys p t r percentage guys is it required that to know which one is p and which one is r not required why because ultimately we are going to multiply them t into r right 5 into 6 or 6 into 5 will it make any difference it doesn't make any difference so type p first of all how much is p twenty thousand in sorry two thousand i'm sorry into t is how much you can type six or five yarish then into five then into pressure percentage so how much it is 600 so the answer for this question is option p you understood you understood okay product of the roots see if i after after i i do the concept called as equation quadratic equation then actually 30 is basically what product of the roots t into r the roots are t and r obviously product of the roots will be 30 so if you know quadratic equation concept then it will be very easy so when i do quadratic equation i'll come back to this question and i'll tell you by looking at the equation only you can say what is part of the roots 30 itself you can straight away feed 2 000 into 30 pressure percentage that's the answer okay since uh oh same question right next question you see which type is this type five of simple interest two amounts in terms of rupees so this is t1 and this is t2 there's shortcut a2 minus a1 divided by t2 minus t1 would you do would you like to multiply with t2 or t1 t2 will do if you multiply with t2 what you need to subtract a2 do it how much 620 option b nice it's not compulsion that you multiply always t1 you can multiply t2 also but if you multiply t2 subtract a2 you get negative answer but you have to take it as modulus of it hope you remember that right shall we move on yeah yes a person wants to lease out a machine guys hope you remember leasing concept a person wants to lose out a machine costing 5 lakh what is 5 lakh pv of purchase correct guys for leasing problem you need pv of purchase and tv of leasing correct what is pv of purchase filak now we need to find what pv of leasing guys leasing is regular or due it is regular annuity regular what's the short what's the formula for ar a into 1 plus i whole power n minus 1 divided by i into 1 plus i whole power n guys hope you remember for present value pro problems after you do 1 plus i whole power n you need to store it why because 1 plus i whole power n it is required for the denominator also now what is i in the question 10 percent that means 0.1 what is 1 plus i 1.1 please type 1.1 in the calculator raise the power to how many years 10 years please raise the power to 10 how do you raise the power to 10 press into keep pressing equal until 11 appears after that don't do minus 1 straight away store that why am i saying store it because 1 plus i whole power n it is there in the denominator as well correct so please store it how do you store it by pressing m plus then do what minus 1 then press the divide by button divided by what i what is i 0.1 what do you do after dividing by i would you multiply or divide again divide why divide it's in denominator right 1 plus i whole power n is in denominator so press the divide by button what is the value where is the value actually in the memory already you have stored it how do you recall by pressing mrc then press equal to then come out of the brackets multiply a what is the a value rent 51272 tell me what it is three lakhs three lakh fifteen thousand forty four three lakh fifteen thousand forty five sorry guys tell me which one is better leasing or purchasing if leasing is better it is favorable for whom it is favorable for lessee if leasing is better it is favorable for lessee not the lesser i have given that note if leasing is better leasing is preferred then it is favorable for whom let's see so the right answer for this question is favorable for lessee is it clear is it clear everyone the calculation part yes just try to learn the calculation that's it don't worry about the concepts right i mean for those attending for the first time not for everyone guys don't take it other way okay shall we have the next question yeah guys we have solved enough questions on leasing yes haven't we we had okay let a person invest a fixed sum at the end of each month in an account paying interest 12 per annum compounded monthly compounded monthly conversion has to be done first of all what is n for monthly compounding come on 12 into number of years how many years they've said huh by default one it is so what is i 12 means 0.12 divided by what 12 so that is 0.01 now if the future value of this annuity after twelfth payment is fifty five thousand guys they have given future value now we need to find what a annuity we need to find so fv is equal to is it regular or due is it regular or due how do you say regular at the end of every month so it is fv of ar what is fv of ar a into 1 plus i whole power n minus 1 divided by i take your calculator what is 1 plus i one guys be very careful it is not 0.12 because monthly so 0 1.01 is 1 plus i value raise the power to what 12 because n is 12 would you store it actually not required why because it is not there in the denominator only for present value problems you will have to store minus 1 divided by i what is i 0.01 now you have to what store it why store because you need to send this value to the left hand side as a denominator what do you do now 55 000 divided by what mrc press what equal to what is the answer approximately four thousand three thirty seven online students no response hope you are doing it guys you got the answers everyone guys future value present value problems perhaps they are easiest problems it will they will not let you think if you know the four formulas of what annuity future value present value future value of a r future value of a d present value of a r and present value of a d you can solve the questions comfortably isn't it clear so we have an expression next question should be a lady one determine the present value of the perpetuity of rupees 50 50 000 per month guys is it an ordinary per repeat what raksha anyways see annuity regular means if the payment is made at the end of every period it could be end of every month end of every half year end of every quarter or end of every year it is said to be annuity regular if the payment is made starting from today or in the beginning of the year in the beginning of the month in the beginning of the half year then it is said to be annuity due if they don't specify about i mean end or in the beginning by default it is annuity regular all right okay fine now look at the question determine the present value of the perpetuity of 50 000 per month at the rate of 12 percent per annum okay now tell me is it a normal perpetuity or a growing perpetuity how do you say normal perpetuity there is no growth rate given only the nominal rate is given what is uh pv of that perpetuity pv of the normal perpetuity is r by i and i told you one thing what is that r by i should be in same terms i normally will be given in terms of per annum right so r also must be expressed per annum but how r is given 50 000 per month they have given how do you convert this into per annum into 12 you have to do so what is it 6 lakh r is 6 lakh so what you should be writing in place of r is not 50 000 it is 6 lakh so type 6 lakh divided by i i is 0.12 what's the result of it 50 lux so answer for this question is option b have you all got the answers guys have you ever got the answers yes shall we move on shall we move on let's just try to get the calculations that's very important okay don't worry about the concepts you can always go back to the concepts right so one more paper i'll solve guys other papers you are supposed to solve right can you do that have you consolidated your doubts no not yet okay fine so another paper i'll solve after that we'll start with a new chapter remaining papers you are supposed to solve there will be two to four papers i think two papers after this and two papers have shared please solve them any doubts consult it and asked me in the class which paper and which question you tell me we will solve it right okay let's have a look at the question rupees 10 000 is invested at eight percent per annum compounded quarterly compounding you have to see properly guys which compounding it is quarterly compounding so quarterly means what is the conversion n is 4 into number of years how many years they have given 2 so what is n 8 i is how much percent 0.08 percent divided by 2 which is 0 sorry 4 i'm sorry because quarterly divided by 4 0.02 now guys what is that we need to find value of the investment that means is it principal or the amount after two years value of the investment after two years means what amount so what is amount formula for compound interest p into 1 plus i whole power n guys here the value given is not proper actually so they have given negative and all so don't worry about if you're not sure about that particular value don't worry about it just solve it what is one plus i one point zero two because i is zero point zero two when you add one to it it'll become one point zero two type one point zero two raise the power to how much eight raise the power to eight one point one seven next into p you do what is p given in the question ten thousand guys what makes you decide that it is this is not a uh future value problem what makes you decide that this is not an annuity problem first of all it is not invested every year they have said what 10 000 invested that's it have they said invested every year had they said invested every year this would have been what annuity problem hope you are getting the difference between annuity problem or simple uh compound interest problems everyone is it clear okay now what's the answer for this eleven thousand eleven thousand seven one six point five nine option b is the answer have you all understood have you all understood shall we have the next question yeah a bank pays 10 rate of interest interest being calculated half yearly conversion is the key first of all what is end for half yearly 2 into number of years how many years they've said 1 year so which is 2 only what is i zero point one divided by what two because for a half year you will get half of the interest given zero point zero five now what is a sum of 400 is deposited in a bank what is 400 p what is asked a correct the amount at the end of one year means obviously amount p p is given a is asked so what is a p into 1 plus i whole parent guys once again the same calculation 1.05 you type in the calculator how do you raise the power to n that is 2 press into press equal to the value get squared then into what principle what is principal given 400 and the answer is 441 option d isn't that easy how many questions on amount formula of a compound interest one here and one here right there will be more questions a certain money doubles itself in 10 years when deposited on simple interest it would triple itself guys what concept type 4 what is the type 4 shortcut a2 minus 1 divided by a1 minus 1 into t1 what is a2 here and what is a1 here a1 is 2 times and a 2 is triple that is 3 times so 3 minus 1 is 2 divided by 2 minus 1 is 1 into what is steven 10 answer is answer is 20 years so if you can identify how many amounts are there in the question two amounts in terms of what principle double is one amount triple is another amount so double a is a1 is equal to 2 a2 is equal to 3 when you see two such amounts in the question you can apply the shortcut a2 minus 1 divided by a1 minus 1 into t1 answer for this question is 20 years clear is that clear everyone online students yeah look at the next question a man deposited eight thousand in a bank for three years at five percent per annum compounded compound interest after three years he will get have this said about the type of compounding in the question already answer is given option d have they specified a type of compounding in the question no if they don't specify the type of compounding default compounding is what annual compounding so n will be same as number of years i will be same as interest rate per annum guys 8000 is the principle what is that we need to calculate amount at the end of 3 years a is equal to p into 1 plus i whole power n what is 1 plus i guys 1.05 because 5 means 0.05 1.05 raise the power to how much 3 into eight thousand answer is nine two six one guys in this slide only three questions are on amount formula of compound interest isn't it in this slide four out of four question three questions are on compound interest that is amount formula only is that clear is it clear everyone everyone if in two years at two years time a principle of 100 amounts to 121 when the interest rate at r percent per annum is compounded annually then the value of r will be guys tell me what is 100 principle what is 121 amount compounded they have given right so which formula connects amount in the principle in case of a ci a is equal to p into 1 plus i whole power n correct now what is a given 121 what is p given 100 and i they have not given so 1 plus i whole power what is n how many years 2 years so n is equal to 2 okay now 121 gets divided by 100 yes or no what is 121 by 100 1.21 now guys 1 plus i whole power 2 how do you calculate this plug in the options that's it what is the easiest option that that you can plug in guys ten percent you can plug in that is the easiest option so type one point one in the calculator if you plug in i as ten percent what is the value of ten percent zero point one 1.1 you type press into press equal to that means square how much do you get 1.21 so therefore i is equal to how much 10 option d have you understood clear is it clear everyone how many problems same appreciation formula four questions so for out of five questions four questions are on appreciation formula only have you understood this online students any doubts explain one so sure listen listen they have given in two years time that is n is equal to two they have given rupees hundred a principle of hundred amounts to 121. so they have only given p is 100 and a is 121 so what is the rate of interest they are asking us it is as per ci what is the formula that connects amount and the principle in case of a ci a is equal to p into 1 plus i whole power n correct now what is a they have given 121 and what is p 100 1 plus i what is n 2 all right now 100 gets divided on the left hand side right 121 by 100 is 1.21 what remains on the right side 1 plus i whole power 2. now what you need to do plug in the option the easiest option that you can think of is 10 percent yes because 10 to 0.1 when you add 1 2 it will become 1.1 type 1.1 in the calculator please do that as a result of 1 plus i raise the power to 2 because whole part 2 is there don't you get 1.21 so therefore i is equal to 10 percent you can do that also is that clear benign now may not is that clear yes let's move on to the next question a sum of money q was deposited for five years and four months at four and a half percent simple interest amounted to 248 then the value of q is q means what principle guys which type amount is given principle is asked which type second type so what is p a divided by 1 plus tr percentage which one do you solve first of all denominator in denominator which one do you feed first of all t into r in time look at the time given months they have given what do you do 4 by 12 plus what 5 because 5 years 4 months they have given first of all months you have to type divided by 12 that will convert the months into years plus the years how much is the years five so this is time you can do this in one step in the calculator then what you do into r what is our given 4.5 press what percentage then plus 1 what do you do with this store it how do you store this by pressing m plus now amount by denominator what is the amount amount is 248 type 248 divided by mrc then press equal to answer is option b have you understood have you understood type 2 of a simple interest amount is given principle is r so p is short cut up you apply the shortcut of type 2 a divided by 1 plus dr person next question should be a laddu for you because it is effective rate of interest in effective rate of interest problem the very first thing that you have to see what compounding what type of a compounding quarterly please tell me what is n 4 into 1 number of years is always taken as what for effective rate of interest 1 so 4 into 1 which is 4 i is 7 means 0.07 divided by 4 which is 0.0175 now what is percentage eri guys 1 plus i whole power n minus 1 whole multiplied by 100 what do you first of all type in your calculator 1.0175 because 1 plus i is i is right here when you add 1 to it it will become 1.0175 raise the power to four you know how to raise the power to four please do it minus one into hundred option d seven point one eight percent 7.18 guys have you all understood have you all got the answers please do let me know yes okay shall we look and look into the next question how much will rupees 25 000 amount in two years again amount formula only yeah what is 25 000 what is 25 000 principle and number of years is two here which which type of compounding ah compound rate of interest are different for different years so which formula would you use a is equal to p into one plus i1 into 1 plus i2 take calculator what do you type in place of 1 plus i1 1.04 into what do you type in place of 1 plus i2 1.05 into the principle which is twenty five thousand answers like two question yes or no if you know it is laddu otherwise boondi make it a laddu and eat understood clear guys shall we move on to the next question everyone everyone shall we move on to the next question yes eight thousand at ten percent per annum interest component half yearly again common formula i think seventh or sixth question on same amount formula on in the same paper which type of compounding half yearly so what is n for halfway compounding two into number of years how many years they have given one year only end of one year which is two what is i zero point one by two which is zero 0.05 what is that they've asked find the amount uh yeah a is equal to p into 1 plus i whole power n what 8 000 very good nice how much time will these kind of questions take 10 seconds take 30 seconds also not a problem you have 72 seconds to solve a question so that is why i'm saying this chapter is very very easy not just easy you can solve the question within the stipulated time you can actually save 50 of the time you can save 50 percent of time from time value of money equations so if you practice all the types so you need not have to look into other materials just my notes that is sufficient the varieties of questions how to identify the questions if you know that and if you know the shortcut tricks uh along with that how to do the calculation in one step in the calculator using m plus m minus mrc that division if you know that easily you can solve the questions right so hope you got used to the calculations now everyone yeah yes or no look at the next question the value of furniture depreciates by 10 a year if the present value of this furniture in an office is 21 870 calculate the value of a furniture three years ago tell me guys three years ago will the value be lesser or more furniture it's a depreciating asset obviously three years ago it will be more tell me in depreciation which value will be more p or a p will be more a will be less so according to the question we need to calculate p or a p so what was given to us they have see there's a deceiving statement in the question what is that present value they have given present value of a furniture is 21 000 870 normally how a student will take it as p but this says whether it is p or a three years ago had the question beans been after three years that twenty one thousand eight seventy itself would have been principal since it is before three years so obviously three years ago the value of a furniture would have would be more than today's value so we need to find what p what is given to us is a so guys a is equal to p into 1 minus i whole power n is a depreciation formula yes or no so what is i 10 i told you how to solve this right 100 minus 10 take 1 as what for depreciation problem 100 100 minus i 10 90 that's still in a percentage what is 90 equal into 0.9 type 0.9 raise the power to what n how many is 3 what do you do after that raising after raising the power store it why because you need to find the value of p after storing it what do you do amount what is amount 21 870 divided by mrc press what equal to what is the answer 30 000 option a you understood haven't we solved questions like this we had depreciation done or not next question if the compound interest on a sum for two years at four percent per annum is one or two ci is given guys simple interest in the same at same rate of interest will be guys i told you when a si for two years is given to find ci which method to be used when a si for for some duration is given if you ask you to find ci for the same duration at the same rate of interest which method to be used no no no no no which method si for two years is given to find ci for the same duration at the same rate of interest what is the method verification method yes it is a verification method that you are supposed to use see be it the other way around bound also they give you ci for two years they ask you to find si for the same duration use again the verification method only hope you remember the verification method how many years they have given two years draw the line split the line into two parts all right now guys they have given ci for two years is one not two s i will be less than one or two or more than one or two because always ci will give you more right okay guys which option you think can be a pause easiest option to pick 100 because it is a moderate value also it is easiest to pick so guys assuming i for two years is hundred what is s i for one year fifty hope you remember the verification method on the top of every year you will write s i for one year right s i for one year will be fifty because you are assuming s i for two years is how much hundred so s i for each year will be fifty fifty on the bottom of every year what do you write difference what is the difference between c i and s for the first year zero what is the difference how do you find out your difference in the second year put the box like this to the left of second year add the numbers into what the rate of interest how much is the rate of interest four percent how much do you get 50 into four percent guys add all the numbers to get the total ci how much do you get one not two how much they have given one not two only so what is si for two years hundred rupees understood please understand guys whenever they give you ci for two years asked us to find s i for two years or s i for two years if they ask you to find ci for the same duration at the same rate of interest always use what verification method hope you remember that yes have you all understood online students difference again okay let me explain again see please understand the concept that they have given the ci for two years as 102 rupees at some rate of interest they're asking us to find s i for the s i on the same sum for the same duration at the same rate of interest so for such problems use what verification method now if you and if you stick to your basics and think okay ci for two years is one or two rupees s i will be less than that or more than that obviously s i will be less so it will not be less by too much it will be less by a small value okay by how much less we will check so uh what is asked si for two years pick the options guys so which is the moderate option and the easiest option you can pick 100 assuming si for two years s i for two years as how much hundred so s i for one year will be 50 rupees we are assuming what s i for two years as 100 because it's one of the option so we draw a line verification method divide the line into how many parts equal to number of years how many years they've said two years so i have divided the line into two parts on the top of every year what i should be writing s i for one year tell me guys if si for two years is 100 rupees what is si for one year 50 and 50 clear now what is the difference between si and the ci for the first year there won't be any difference because both si and i will be same because principle will remain the same if the principle is same there is no difference between principle i mean s i and c i okay therefore the difference for the first year is zero what is difference for the second year to the left of second year whatever numbers you have add them 50 plus 0 is 50 into how much percent four percent what is 15 to four percent two now to get the total ci what i said add all the numbers on the top at the bottom 50 plus 50 hundred hundred plus zero plus two one not two what does that will be ci and haven't they given c i as one or two rupees correct it's one or two only right ci is one or two so we started with sr we arrived at ci which is one not two given in the question so therefore the answer is option b hundred have you understood everyone clear not clear yes look at the next question ladoo difference between two years what is p difference for two years divided by i square what is different for 2 years given 372 type 372 divided by what is i 0.1 equal to how many times 2 times and the answer is thirty 30 seven thousand two hundred clear clear everyone see for two year and three year difference use the shortcut that i have given for more than three years apply the conventional method conventional method also will give you the answer 30 40 seconds not more than that right next question probably the last question i guess what is the net present value of the piece of property which would be valued at 2 lakh at the end of 2 years tell me what is 2 lakh guys future value what we need to find its present value that is what the question what is the relationship between future value and present value if you forgo forget that formula always you can get the relationship between future value and present value by which concept p is equal to a is equal to appreciation formula guys in appreciation formula a is equal to p into 1 plus i whole power n which is future value amount of a is the future value correct and what is p present value fv is equal to pv into 1 plus i whole power n what is that we are asked to find pv or fe present value so therefore pv is what fv divided by 1 plus i whole power n let's take your calculator what is fb given 2 lakh type 2 lakh type 2 lakh divided by what is 1 plus i guys 1.05 this equal to how many times press equal to how many times two times why because two years right what is the answer 1.81 likes have you all understood have you all understood is it 1.81 lakhs is there any question you saw that it takes pages to solve it is there any question which takes one page to solve one line answers yes or no two papers i think successfully we have completed papers will be like this only be clear with the concepts and the shortcuts type identification is very very important that is the key in the chapter yes am i clear is it clear yeah one lakh eighty one thousand four not five yes one point eight one lakhs is it clear everyone yeah guys two more paper in this and two papers i have shared please do that before solving the papers make sure the concepts are in your mind if the concepts are there in your mind then solving questions will be very very easy it's just that you have to practice art that's it 20 20 december of which question you tell me the ratio of principle for three years 216 is these three questions okay we'll discuss this okay don't worry look at the question guys the ratio of principle and ci value for three years what is that they have given ratio of principle and ci that means p by c i correct ratio of principle and c i means p by c i s or no okay i'll write p only what is c i guys p into 1 plus i whole power n minus 1 can i write like that what is that equal to according to them it's 2 1 6 divided by 127 correct correct 216 divided by 127 is it clear everyone now listen pp cancels pp cancels guys whole power n where do you have in the denominator or in the numerator denominator so how do you get that to numerator take the reciprocals on both sides can you do that yes if you have 1 by x is equal to 1 by 2 if you want to find the value of x you take the reciprocal on both sides 1 by x becomes x 1 by 2 becomes 2 correct same way take the reciprocal on both the sides what happens 1 plus i whole power n minus 1 is equal to 127 by 216 what is 1217 by 216 how much 0.58 and minus 1 if it is taken on the right hand side will become plus one add one to it one point five eight seven nine okay now what is that they've asked is the rate of interest guys n is given right n is how much three years n is three years now what you need to do is plug in the options guys what is the moderate option that you can plug in there's no moderate actually right just plug in the options which option satisfies this have you given the rate of interest so i mean option c see tell me are these values of i are percentage values to the fractional values ah the fractional values you need not convert them into percentage i mean fraction they have not given in terms of what have they given that in terms of percentages no they're all fractional values option ena option c guys plug in option c 1.1666 type that 1.1666 raise the power to 3. one point five eight seven six so clearly option c is the answer option hitting method here it's option c guys what is that they have given in the question is the ratio of principle and ci ratio means numerator by denominator principle is in the numerator and ci in the denominator write down ci in terms of principle p into 1 plus i whole power n minus 1 p p cancels and 1 plus i whole power n is in the denominator since you need to find the value of i take that to the numerator how do you take that to the numerator by taking the reciprocal on both the sides so 1 plus i whole power n minus 1 will go to the numerator and 2 1 6 by 1 27 becomes 127 by 2 1 6. the reciprocals then minus 1 goes on the other side becomes plus 1 already you know 127 by 216 is 0.587 when one is added to it will become 1.587 all that you have to do is plug in the options that's it clear is that clear is that clear yeah which is the other question you are asking ah okay look at the next question an amount is lent at a nominal rate of 4.5 percent per annum compounded quarterly conversion has to be proper n is equal to 4 into number of years how many years they have given 1 they haven't specified the number of years right so what is i 0.045 4.5 means 0.045 divided by what four so what is that zero point zero one one one two five ah zero one one two five okay now what do you do what would be the gain in the in rupees over when the when compounded annually just tell me for annual compounding you get more or for quarterly compounding you get more more the number of compoundings more the number of times the principle is going to change obviously more is the returns more the number of compoundings more will be the returns so what you need to do is find out amount in the first case amount in the second case what are the cases here one is quarterly compounding the other one is annual compounding please find it out a is equal to p into 1 plus i whole power n this is for quarterly do it for quarterly first of all what is 1 plus i 1.01125 raise the power to 4 into p what is p assuming assuming p as thousand they're only given what is it thousand forty five point five seven six okay now what next a is equal to p into 1 plus i whole power 1 thousand 45 1.045 so this is this is for annual compounding this is the quarterly compounding the difference the gain is obviously the difference so which one is the right answer 0.76 is gain again in which case actually quarterly compounding or annual compounding quarterly compounding is giving you more obviously by how much 0.76 rupees more so option c is the right answer yes option c correct that's all or you have more questions in this last one you deposit rupees 900 per month into an account that pays 14.8 percent compounded monthly convert i and n what is n 12 into number of years how many years they've said nine months correct nine months means how many years so do you have to convert actually not required because it is in terms of months only right n will be simply nine right nine months what will be i fourteen point eight percent mean zero point one four eight divided by twelve tell me how much it is one two three uh zero point zero one two three now what you need what do you need to find amount right p into one plus i whole power n guys is there any doubt y n is nine only listen here right what is n conversion monthly compounding 12 into number of years 9 months equal into number of years how much 9 by 12 please do it how much it is 0.75 what is 12 into 0.75 9 only and basically what number of compounding it's monthly compounding they have given nine months obviously nine times the principal is gonna change right so it's nine only what is the answer beer dear is it thousand check once one should be thousand only no one point zero one two three raise the power to how much nine into p that is nine hundred so nearest answer is only thousand option d what was the doubt in this question n it's not nine years nine months no so nine times the principle is going to change are we done a machine with find the scrap value of the machine if the life is six years okay options that's okay fine listen the refrigerator costs 40 000 today what would be its cost how to identify a depreciation problem or future value present value problem that's what your question is right okay look at the first question they've clearly specified the machine depreciates at what 10 per annum so this is clearly a depreciation problem and they have clearly specified as crap value in the question look at the second question have you said about deprecia yeah refrigerator is a depreciating asset but have they said it is depreciating they haven't said about depreciation what is that they have asked what would be its cost after two years if you want to purchase the same one after two years what would be its cash so how to identify how do you differentiate a depreciation problem and other problems as appreciation problems is they should clearly specify depreciation rate if they don't say depreciation rate it is not a depreciation problem so they they mean to ask what would be the cost of the same refrigerator if you want to purchase brand new after two years what would be the value of the um a is equal to p into 1 minus i whole power and that is appreciation appreciation is p into 1 plus i whole part so according to this the value after two years if you want to purchase the same refrigerator after two years because of inflation rate it will be more than 40 000 but if you apply a depreciation concept here it will be less than 40 000 so please understand how to differentiate depreciation problems that definitely they'll specify depreciation rate if they don't specify depreciation rate apply appreciation concept only so that is the hint point to identify appreciation problem and depreciation problem clear guys any doubts online students you can ask me guys one more problem a sum of rupees 41 fifty years in six years at certain rate of interest per annum interest compounded annually what is the x actually here principal value of x is options are there yeah tell me 16 080 all right 18 600 all right 18 060. 16 800. guys you can discuss later okay let us look into this problem a sum of rupees i mean x rupees amounts to twenty seven thousand to nine hundred in how many years three years and forty one thousand eight fifteen how many years six years don't you think there are two amounts and two cases yeah one amount a is equal to twenty seven thousand nine hundred appreciation formula y appreciation formula because amount is given and it is as per ci that's most important so p into 1 plus i how many years the first amount is 3 years yeah can i write so for the first case equation one second case amount is how much forty one thousand eight fifty and that is equal to p into one plus i how many years they have given for the second case six years all right is it clear so far clear now guys there are two unknowns one is p the other one is i how do you eliminate p by dividing or adding a what dividing two by one or one by two two by one why because second amount is more than the first amount divide forty one thousand eight 850 by 27 900 how much is it 1.5 you know p p cancels in the numerator 1 plus i whole power 6 in the denominator 1 plus i whole path 3 the result of that will be 1 plus i whole power 3 only correct any doubt so far any doubt so far what is the question asked to find the principle right x is the principle isn't it you need to find the value of principle there is 1 plus i whole path 3 is how much we got 1.5 i think you got till here right you would have solved this still here you need to find the principle look at the first equation you have 1 plus i whole power 3 in place of 1 plus i whole power 3 can't we substitute 1.5 you can only that thing you have not done i guess yes so equation 1 implies 27 900 is equal to p into 1 plus i whole power 3 values how much 1.5 so therefore what is p 18 600 option so this step you did not think of doing it right yeah okay see what is the question asked it is not one plus i value or n value n value given of i value they have not asked actually all right what they have asked is the principle x means what principle okay so we got by dividing equation 2 and 1 what did we get 1 plus i whole power 3 is 1.5 can't we substitute 1 plus a whole path 3 value in the first equation and solve for p see what is equation 1 actually 27 900 equal to p into 1 plus i whole power 3 in place of 1 plus i whole path 3 we can substitute 1.5 and we get the unknown value that is p how much 18 600 that's understood everyone yes sometimes an extra step you have to think you know everything you just have to think right don't be restricted within a box think out of the box just apply the basics that's it you know 1 plus i hold part 3 is 1.5 that value has to be substituted here online students is that clear the problem i think this page this question was asked in 2021 july i'm not wrong 2021 july yes shall we move on we are done with the chapter okay so please solve the rest of the papers any doubts consolidate and ask me make sure none of the questions should be left unsolved if you are thorough with all the questions take it from me scoring out of out from the chapter tvm is very easy guys 12 to 16 marks is not a small number it is not a small number at all and you saw most of the question 90 percent of the question will take only 10 to 15 seconds it won't take much time right if you solve it conventionally yes it will take more than two minutes also if you solve it but you saw most of the previous paper question how much time it took right so only thing is that the concept should be clear the clarity should be there practice a lot right if you practice a lot obviously you can solve the questions easily the concept should be clear that's it all right okay [Music]