[Music] good day everyone so in this video lesson we will discuss about simple annuity so pakistan is for example our payment uh interval period so for example so but i'm focused not in neon it's about simple energy okay so you know application application on topic so our objectives is to illustrate simple and general annuities distinguish between simple and general entities find the future and present values of simple entities and compute the periodic payment of simple entities so when it says periodic payment so your new amount is nothing so we're going to uh illustrate simple and general address if there is according to payment interval and interest period simple entity this is an annuity where the payment interval is the same as the interest period so um in general annuities of this annuity where the payment interval is not the same as the interest period so in this last saying but according to time payment amount time of payment so now be nothing ordinary entity or that is the annuity immediate is a type of annuity in which the payment are made at the end of each payment interval and then pakis a type of annuity in which the payments are made at the beginning of its payment interval but according to duration annuity certains and annuity in this payment begin at the end of definite times at pakistan contingent annuity an already in which the payment extend over an indefinite or indeterminate length of time also we need to familiarize some of the definition of terms now may encounter natanza vigilance or satapic nato first the term of an already denoted a small letter t that is time between the first payment interval and the last payment interval regular or periodic payment denoted as capital letter r so the amount of each payment amount or the future value of annuity denoted as capital letter f that is the sum of future values of all the payments to be made during the entire term of the annuity present value of an annuity are denoted as capital letter p that is the sum of present value of all the payments to be made during the entire term of the annuity so what are those formula now meeting attend you know in this video lesson in this topic first to find the future value of simple ordinary energy that is r or the regular payment times the quantity of 1 plus i raised to n minus 1 over i and paco ninomenation present value of simple energy so regular payment times one minus the quantity of one plus i raised to negative n over i where your i that is r over m so you are nothing that is the interest rate at your m not n that is the frequency of conversion no and then spug rs that is the regular payment i that is the interest rate per period so panning continue i that is rate the interest rate over the uh frequency of conversion so n is the total number of payments so n that is m times t r is the nominal rate okay or yes this is the interest rate and m is the number of conversion periods pakukuni nominated in periodic payment depending upon given a uh nandunion future value so on gagamitin atom to compute the regular payment or the periodic payment is f over uh the quantity of one plus i raised to n minus one over i pero capa given the minimum present value ethernet for millennia p over 1 minus the quantity of 1 plus i raised to negative n over i and then okay so let's try determine if the given situation represents simple annuity or general energy letter a payments are made at the end of each month for a loan that charges 1.05 interest compounded quarter d letter b a deposit of 5 500 pesos was made at the end of every 3 months to an account that earned 5.6 interest compounded quarterly so selector a so i'm beating the net in general payment interval interest period so in payment interval nothing details letter a is every month period interest period nothing is quarterly therefore hindi si la pareho so what kind of uh the situation represent as general and with because they are not equal a letter b so an impairment of interval that is a letter b so it's a letter b every three months so every three months so a b sub n that is quarterly and then the interest period is compounded quarterly so equals equaling per uh payment and variables interest period and so therefore uh that this uh situation no is an example of simple annuity okay and then i think about simple annuity that pakistan simple annuity equaling payment interval and the interest period another determine whether the situation describe an ordinary entity or an annuity jew letter a june's monthly mortgage may meant is 35 000 148 at the end of each month okay so letter b the rent of apartment is 7 000 pesos in june at the beginning of each month so selector a what do you think so i'm payment is at the end of each month so therefore the answer is ordinary annuity so selector binance is ju at the beginning so you at the beginning so therefore that is an example of anvitiju okay so next example number three suppose mrs remoto would like to save three thousand every month in a fund that gives nine percent compounded monthly how much is the amount of the future value of their savings after six months so first we need to uh identify the given so tinder nathan has so in payment of interrupt is every month and then your interest period is compounded monthly so they are equal so this situation illustrate that this is an example of simple annuity okay so animal given a 10 so regular payment name mrs remote is 3 000 then the interest rate is nine percent or that is 0.09 and the term or the time that is six months or that is one half years no or 0.5 years and then uh the frequency of conversion since that is compounded monthly so therefore young m nothing is 12. young n not n that is m times t or uh the frequency of conversion times term so since we have 12 sixth month is equivalent to one half years tama so he converted it to in a year six month uh divide 12 blaneno here so 12 times one half since young tina ten is one half that is six so young and nothing is six and then i not n that is r over m 0.09 divide 12 the answer is 0.0075 okay so after getting all the given values on future values what is the amount of how much is the amount of the future value so what is the formula up again happening in future value so regular payment plus 1 plus i raised to n minus 1 over i so what you're going to do is uh you need a scientific calculator or a calculator okay and here up you compute to manually so that will become three thousand times one plus zero point zero zero seven five raised to six minus one okay so you know what nothing you might even attend formulas over zero point zero zero seven five so and that is using your scientific calculator the answer is eighteen thousand three hundred forty point eighty nine okay so using the calculator sopano gaga meeting using the calculator okay so using the calculator by using the calculator so panning a uh input learn the hat so first the new production bar and then clicking it on left iron at all and type name 3 thousand and then put that on open parenthesis okay more one point zero zero seven five close parenthesis and then jump exponent that is six and then next tile baba muyan next minus 1 and then sababa type meow 0.0075 and then equals so the answer is 1840.89 so you can use your scientific calculator no parameter okay next in order to save for her high school graduation murray decided to say 200 pesos at the end of each month if the bank pays 0.25 percent compounded monthly how much will her money be at the end of six years so thinking i think on simple android so high school graduation so each month your payment interval so and then compounded monthly so they are equal so this is uh this situation is illustrate simple annuity so animal given attend some regular payment is 200 pesos and the new interest rate is 0.25 percent that will be 0.0025 so you could convert the nation into decimal and then the term is 6 years and m is 12 since that is compounded month d and then n not n m times t or that is 12 times 6 that is 72 total number of periods and i are over m that is 0.0025 divide 12 so [Music] and then using the formula so in hana playing that is future value so using the formula is a subtitle in all the given values of 4 million atom 200 times 1 plus this is our i 0.0025 over 12 raised to 72 minus 1 all over 0.0025 over twelve so you can uh a check using your calculator so again faction bar muna so hop okay class you can use uh in the 2013 fraction 0.0025 times over 12 and then okay close parenthesis spin the thing in production bar i don't know close and then production bar i know exponent 72 minus one and then detail again another fraction that is zero point zero zero two five over twelve and then pin the thing around equals so the answer is fourteen thousand five hundred seven point zero two so nine out of nine okay rose works very hard because she wants to have enough money in her retirement account when she reached the age 60 so she wants to withdraw 36 000 every three months for 20 years starting three months after she retires how much rose deposit at retirement at twelve percent per year compounded quarterly for the annuity so analyze nothing in problem so you don't make 130 six thousand every month so ebik said being that 36 000 is the future value or the future amount right so so your regular payments is 36 000 no and then on rate not indeed 0.12 and this 20 years okay again and a hand up that they need this future value rights and then and given that is 36 thousand and then n is 80 or m times t that is 80 and your i not in a 0.12 wide that's 12 percent converted into decimal so 0.12 divide four so then you learning formula class okay important thing i'm uh identifying you making a game with nothing no variable for your formulas the answer is zero point zero three okay since angie nahan have not indeed a present your regular payment is 36 thousand so therefore i'm gonna hand up that is present value using the formula so that is thirty six thousand times one minus one plus zero 0.03 raised to negative 80 over 0.03 and the answer is 1 million 87 and 227.48 check using the calculator so that is 36 000 and then 1 minus that was open parenthesis 1.03 and raised to negative 80 and it's alba that is divided by 0.03 so the answer is i okay but okay wrong so little so that is 36 000 the regular payment this one minus one point zero three two and raise two point by exponent that then that is negative eighty all over 0.03 so equals that is one million eighty seven thousand two hundred use a point forty correct okay so that is for uh example number five and for another example the cash value or the cash price of a purchase is equal to the down payment if there is any or plus the present value of the installment payment so pankinopoulos down payment plus the present value so pano going in for example mr ribaya paid 200 000 as down payment for a car the remaining amount is to be settled by paying 16 200 at the end of each month for five years so if interest is 10.5 percent compounded monthly what is the cost price of his car so a big sabine class uh may not buy the two hundred thousand pesos and then your remaining payment baba yaran yes so now my down payment time two hundred thousand regular payment is six thousand two hundred the interest rate is zero point one zero five since that is ten point five percent convert into decimal and the term is five years and the frequency of conversion is 12 since monthly and n m times t that is 12 times 5 is equal to 60 so i not in d is r over m or 0.105 divide 12 and that is equal to 0.00875 okay surprise price price that is the down payment plus the present value so in present value using the formula substitute all the given values sixteen thousand two hundred times one minus one plus zero point zero zero eight seven five raised to negative sixty over zero point zero zero eight seven five and the answer is 753 thousand seven hundred two point twenty so union present value so mark one nothing and then cash value or the cash price that is down payment plus the present value so maritime down payment at two hundred thousand plus the present value so mccannion cash price no car the cash price or the cash value is 953 thousand seven hundred two point twenty all right so uh using the calculator check nothing and present value 16 200 okay that is one minus one point zero zero eight seven five close parenthesis thousand pi exponent nothing that is negative sixty all over 0.008 75 okay in equals long equals so the answer is 75 753 point twenty nine not just in it out of the nation and then plus two hundred plus two hundred thousand okay plus two hundred thousand answer is nine hundred fifty three thousand seven hundred point twenty okay so malino next for example number seven paulo borrowed one hundred thousand he agrees to pay the principal plus interest by paying an annual amount of money of an equal amount of money each year for three years what should be his annual payment if there is eight percent compounded annually so in highlight annual payment 100 000 that is the pres that is a present value okay so present value is 100 000 and interest rate nothing is eight percent that is 0.08 the time is three years or the term compounded and m nothing is one n is equal to m times t or three times one is equal to three and the young interest rate period of the month is r over m or zero point zero eight divide one the answer is 0.08 since i'm given nothing's uh present value so we're going to use a to find the regular payment now given your present value okay and that is r is equal to p over 1 minus 1 plus i minus a raised to negative n over i so that's use your calculator so the answer will be thirty eight thousand eight hundred three point thirty five so i don't eat mixed opinions a problem so every year okay so every year mercury amount the presenter paid equal amount of money okay so every year's magma by 738 803.35 so using your calculator it took less gamma tube calculator magog lunacy calculator data the same and then balika and then fraction alert okay you now go in your class then one minus okay one minus 1.08 doubles close then exponent that then negative 3 over 0.08 so the answer will be 3 uh 38 380 why one cool long cigarette ah okay so wait only tinker so 10 000 100 000 so the answer is 38 800 3.35 again please repeat using scientific calculators parenthesis okay so the regular payment against 38 803.35 next another example mr ribaya would like to save 500 000 pesos for his sand college education how much should be he deposits like to say 500 000 pesos save them five hundred thousand pesos eb7 union future value in future amount no so therefore the given is the future value 500 000 pesos rate is 0.01 the term is 12 years and uh the frequency of conversion is two so you'll end up in m times two that is two times twelve so twenty four now a big sub n twenty four times mag and nothing at all [Music] 0.01 divided answer is point zero zero five so since i'm given that in a ninja young future value a tangent hand up nothing is in periodic payment or in regular payment attenuation so therefore gaga mitigating formula is f over one plus i raised to n minus one over i so you can substitute everything there's a given value snap n and the answer is nineteen thousand six hundred sixty point thirty one e big are being plus 24 times number by semester abaya 19 660.31 or every six months so every six months magma magbabayan started buying a nineteen thousand six hundred sixty point thirty one but i'm a consumption of five hundred thousand foreign all right so using the calculator again parama sundan so type [Music] production bar and then type in 1.005 okay then pan exponent that then 1.005 so 24 and then down minus one and then here is zero point zero zero five so the answer is nineteen thousand six hundred sixty point thirty one centimeter nothing can say uh pipe number ten zero thirty 31 okay so you can use your scientific calculator thank you for watching this video i hope you learned something don't forget to like subscribe and hit the bell button put updated ko for more video tutorial this is your guide in learning your mod lesson your walmart channel