If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content
Current time:0:00Total duration:8:17

Video transcript

whenever we talk about money the amount of money is not the only thing that matters what also matters is when you have to get or when you have to give the money so to think about this or to make it a little bit more concrete let's assume that we live in a world that if you put money in a bank you are guaranteed ten percent Interest ten percent risk risk free interest in a bank and this is high by historical standards but it'll make our math easy so let's just assume that you can always get ten percent risk-free interest in the bank now given that let me throw out scenarios and have you think about which of these that you would most want so I could give you $100 right now that's option one I could in one year instead of giving you the hundred dollars immediately in one year I could give you I could give you one hundred and nine dollars and then in two years in two years this is kind of option three I'd be willing to give you one hundred one hundred and twenty dollars so your choice is someone walks up you up to the street I can give you a hundred dollar bill now one hundred nine dollar bill it $109 one hundred nine dollars in a year or 120 dollars two years from now and you know in the back of your mind you can get 10% risk-free interest so given that you don't have an immediate need for money you're assuming that this money you will save that you don't have to you know that you don't have a bill to pay immediately which of these things are the most desirable which of these would you most want to have well if you just cared about the absolute value or the absolute amount of the money you would say hey look $120 that's the biggest amount of money I'm going to take that one because that's just the biggest number but you probably have in the back of your mind well they I'm getting that later so there's maybe something I'm losing out there and you'd be right you'd be losing out on the opportunity to get the ten percent risk-free interest if you were to get the money earlier and if you want to if you wanted to compare them directly the thought process would be well let's see if I got if I took option one if i got the hundred dollars and if you were to put it in the bank what would that grow what would that grow to based on that ten percent risk-free interest well after one year ten percent of a hundred dollars is ten dollars so you would get ten dollars in interest so after one year your entire savings in the bank will now be one hundred and ten dollars so just doing that little exercise we actually see that a hundred dollars given now put it in the bank at ten percent of risk free will actually turn into one hundred ten dollars a year from now which is better than the hundred and nine dollars one year from now so given this scenario or given this kind of situation or this option you would rather do this then do this your better a year from now you're better off by a dollar what about two years from now well if you take that hundred dollars after one year it becomes one hundred ten dollars then ten percent of 110 is eleven dollars is $11 so you want to add eleven dollars to it and so it becomes it becomes one hundred and twenty one dollars so once again you're better off taking the hundred dollars investing it in the bank risk-free ten percent per year it turns into one hundred and twenty one dollars that is a better situation than just someone guaranteeing you to give the one hundred twenty dollars in two years once again you are better off by a dollar and so this idea that not just the amount matters but when you get it this idea is called the time value of money time time value of money or another way to think about it is think about what the value of this money is over time given some expected interest rate and when you do that you can compare this money to equal amounts of money at some future date now another way of thinking about the time value or I guess another related concept to the time value of money is the idea of present value present present value and maybe I'll talk about present and future value so present present and future value future value so given this assumption this 110 this 10 percent assumption if I if someone to ask you what is the present value of a hundred and twenty one dollars two years in the future you would that's they're essentially asking you so let's so what is the present value so the present PV stands for present value so what is the present value of one hundred twenty one dollars two years in the future that's equivalent to asking what type of money or what amount of money would you have to put in the bank risk-free over the next two years to get one hundred twenty one dollars and we know that if you put a hundred dollars in the bank for two years at ten percent risk-free you would get one hundred and twenty one dollars so the present value here the present value of one hundred and twenty one dollars is the hundred dollars or another way to think about present and future value if someone were to ask what is the future value so what is the future value of this hundred dollars in one year so in one year well if you put if you get ten percent of the bank that's guaranteed its future value is 100 to ten dollars after two years it's two year future value is one hundred and twenty one dollars and so with that in mind let me give you one slightly more interesting problem so let's say that I have let's say we're going to assume this the whole time that makes our math easy a 10 percent risk-free interest and let's say that someone says that they're willing to give us they're willing to give us sixty five dollars in one year and we were to ask ourselves what is the present value of this so what is the present value what is the present value of this so remember the present value is just asking you what a mount of money that if you were to put it in the bank at this risk-free interest would be equivalent to this sixty five dollars which of these two are equivalent to you and so you would say well look whatever amount of money that is let's call that X whatever amount of money that is x if I grow it by ten percent that's literally I'm taking X plus ten percent x plus let me write it this way plus ten percent times X let me write not let me make it clear this way X X plus 10% of X should be equal to our $65 if I take if I take the amount I get 10% of that amount over the near that should be equal to $65 and this is the same thing as 1 X or we could say that 1 X plus 10% is the same thing as 0.1 0 X is equal to 65 or you add these two 1.10 X is equal to 65 and if you want to solve for the actual amount of the present value here you would just divide both sides by the 1.10 and so you get X is equal to let me let me do it this way be a little bit more clear about it so let's divide both sides by 1 point and really that trailing zero doesn't matter we're not really too worried about the precision here because this isn't this is actually exactly 10% so this is going to be these cancel out and X is going to be equal to we get the calculator out X is going to be equal to 65 divided by 1.1 $59.09 rounding it so X X is equal to $59.09 which was the present value of $65 in one year or another way to think about it is if you wanted to know what the future value of $59.09 is in one year assuming that 10% interest you would get $65