# Time value of money | Interest and debt | Finance & Capital Markets | Khan Academy

When it comes to money The only thing that is always important is not the amount of money. What matters is when you earn the money or when you give. So let's think about it or a little more Let's assume that we live in a world where When you put money in the bank, the bank tells you 10% risk-free interest rate guarantee. This is high by historical standards, but it makes it easier for us to calculate. So suppose you always leave the bank You get 10% risk-free interest. Now, with that in mind, I'm putting the scenarios aside and which of you do most of them Think what you want.

So I could give you \$ 100 right now. This is the first choice. \$ 100 to you immediately instead of giving it to you in 1 year I could pay \$ 109 and in the next 2 years this is the 3rd choice, to you I'd like to pay \$ 120, and if that's your choice, someone is coming towards you on the street. I can lend you \$ 100 now, or \$ 109 (laughs) Borrow \$ 109 in 1 year, \$ 120 in 2 years and in your mind You can get 10% risk-free interest. Given that you do not need money immediately. We assume you will save money.

Because you do not have to pay immediately. Which of the following is most desirable? Which of these do you want to get more of? If you have the full cost or the full amount of money If you want to know, you will say "Hey, look. \$ 120, that's the most money." "I'll take it because that's the biggest figure." But probably in your mind "Well, I'll take it later, maybe am i missing something? " You will be right. If you took the money quickly, you would You would lose the opportunity to earn 10% risk-free income. If you compare them directly if you wanted, the process would be like this, "Well, let's see. If I take the first option, I'll get \$ 100." If you put it in a bank, How much will it increase based on a 10% risk-free percentage? After 1 year, 10% of \$ 100 is \$ 10. So you get a \$ 10 profit. So, after 1 year in your bank your deposit will be \$ 110. So, just by doing a little work we really saw that the bank was \$ 100 with a 10% risk-free return 1 year later we turned it into \$ 110.

which is better than getting \$ 109 after 1 year. According to this scenario, or given such a situation or, alternatively, to do so you would like more. 1 year later you are ahead with \$ 1. What about 2 years later? If you choose this, \$ 100 is \$ 110 after 1 year will be, then 10% of \$ 110 is \$ 11. You will want to add \$ 11 to it, so it will be \$ 121. Thus, he once again put \$ 100 in the bank with risk-free interest, It is better to choose to earn 10% per annum.

It will be \$ 121. And this is for any of you From the guarantee that he will pay \$ 121 in 2 years is a better situation. Once again, you are ahead with \$ 1. So this idea is not just about the amount, but when you get that, that's the idea called the time value of money. Time value of money. Or another way of not thinking about it is to think about what the value of this money is over time. According to some expected interest rates and in doing so the money is equal to the future you can compare the amount of money. Now, another way to understand the value of time way or another of the approximate time value of money The concept is the idea of ​​current value, current value. Maybe I'm talking about current and future value. Current and future value. Thus, based on these assumptions, this 10% assumption, if someone asks you, “After 2 years What is the current value of \$ 121? " They are essentially asking you What is the current value? CD means current value. What is the current value of \$ 121 after 2 years? That's \$ 121 with no risk for the next 2 years what type of money or how much money to earn is equivalent to asking what is required. We know that. If you put \$ 100 in the bank, After 2 years, you will get \$ 121 with 10% risk-free income. The current value here The current value of \$ 121 is \$ 100. Or a way to think about current and future value if someone asks you what the future holds? So what is the future value of \$ 100 in 1 year? So in 1 year. If the bank charges you 10% if guaranteed, the future value is \$ 110. After 2 years, the future value of 2 years is \$ 121. So, considering these, you let me report a more interesting problem.

So let's say ….. We simplify the calculations during this period We will estimate a 10% risk-free interest rate. Suppose someone tells us in 1 year Will give \$ 65 and we ask ourselves, "What is the current value of this?" So what is its current value. Remember, the current value is just the amount of money you ask asks, that is, if you bank it If you put it at a risk-free interest rate, Will it be equal to \$ 65? Which of these 2 is equal to you? You will say, "Well, look. What is the amount of money?" Let's call it X. No matter what the amount of money, if I If I increase it by 10%, it really is X + 10% X + … let's write. + 10% xX … Let me clarify this way. X + 10% X should be equal to \$ 65. If I receive 10% of this amount during the year it should be equal to \$ 65. It's the same with 1X or we can say that 1X + 10% 0.10X is equal to 65 is the same as, or add these 2. 1.10X = 65, if you have a real current value here if you want to solve you just need to divide both sides by 1.10. We come to the conclusion that X is equal …

So let's solve it. This will be clearer. So divide both sides by 1.0 and really 0 doesn't matter. We do not worry about accuracy, because it is exactly 10%. So it will be … they will be reduced and X will be equal to … Let's calculate with a calculator, X will be equal to 65:11, that is, \$ 59.09, let's round it up. So X = 59.09 which is \$ 65 1 is the current value of the year.

or another way of thinking about it, if the 1-year future value of \$ 59.09 If you want to know what will happen, for 10% of income You will receive \$ 65..