what if I offered you a choice you can either have $100 today or you can have $100 one year from today which one of these would you choose I'm willing to bet that you would pick $100 today why would I wait to have $1100 a year from today when I could just have $100 right now give me the opportunity to change your mind I'm going to slightly modify my original offer now I'm going to offer you either $100 today or you can have $12 one year from today which option will you choose now I'm willing to bet that you would still pick the $100 today because $2 a year from today probably doesn't make it worth it to forego the $100 that you could have right now it seems as though I haven't found the right offer for you yet but let me entice you with perhaps an even sweeter offer I will either give you $100 today or $110 one year from today which will you choose I'm willing to bet that I have now made the future value high enough that you would prefer to have $110 one year from today over just $100 today we now know that my $110 was a very appealing offer perhaps too appealing so what would be the amount of money that would make you completely indifferent between taking my money today versus in the future let's say that if I offered you 100 today versus 100 SP $6 in the future you are pretty much indifferent towards both of these decisions we have just found your time value of money so now that we know that $6 is the amount that I have to add to the $100 to make you indifferent towards taking the money today versus one year from today we can just do some simple math and take 6 ided 100 and find that the interest rate for our time value of money is 6% now that we know our time value of money let's go over some really simple math here we're looking at our formula for future value which we'll call FV it is equal to the present value multiplied by 1 + r the interest rate to the exponent of n which is the number of years so in our example it was our future value of $16 was equal to our present value of $100 multiplied by 1 plus and we said our interest rate was 6% to just one year because we're looking at a onee time Horizon we could State the same formula in a different way and start with future value and work back to our present value so here we're going to see that our present value PV is going to be equal to our future value of $16 divided by 1 plus the interest rate of 6% to the exponent of the number of years which was just one and that brings us back to our present value of $100 today now keep in mind that your time value of money is still 6% so I'm going to offer you one more choice I will either give you $100 today or I will give you $118 3 years from today which of these two options do you prefer you might be tempted to think well my interest rate 6% that means I get $6 a year so three years of $6 a year I end up with an $18 of interest and so $118 should be equal to $100 today but that's not the case because interest compounds so let's use a financial calculator to find out which of these two options you actually prefer to answer the question of whether you would prefer a a $100 lump sum payment today versus a $118 lump sump payment 3 years from today at a 6% rate of interest we can use a financial calculator to simplify our work and if you have a Texas Instruments ba2 Plus calculator the buttons on your calculator should look exactly the same as the buttons on the one on my screen right now what we could do is we could punch in all our values because we already know present value the rate of return and and the number of years and find future value that way or we can use these five buttons on our calculator right here so let's do it with these five buttons so we know three is our number of years and then our interest per year iy is 6% so let's hit six and then interest per year our present value is $100 our payment this is the coupon the coupon payment on a bond and this is just a zeroc cpon lump sum payment that we've been talking about this whole time so payment is going to be equal to zero and now future value is what we can compute for so we'll hit compute future value and that we find that at a 6% of rate of interest $100 should turn into $119 and 10 cents three years from now so would I rather have $100 today or $118 in three years I would rather have $100 today [Music]