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

Background speaker Whenever we talk about money Money is not the only thing that matters Another important thing is when you get it Or when you have to pay it back is important. So think about it or at least a little bit We need to make it stronger. Suppose we live in a world You save money in a bank, you insure 10% effective, 10% safe bank. Historically, it will be high But it makes our numbers easier. So let's assume you always You can get 10% security in the bank. Forget about our fantasies And do you think about such things? What do you want most? So I'm going to give you \$ 100 now This is an option. \$ 100 a year for you Within a year instead of immediately I can give you \$ 109. And within two years This is the third option.

I would like to pay you \$ 120 So your choice It is as if someone on the street were walking toward you. I can pay you \$ 100. \$ 109 (Laughs) Bill \$ 109; \$ 109 a year; Starting at \$ 120 in two years You know, behind your mind You get 10% security. So if you do not need as much money as you give We will accept it as your savings. If you do not have to pay immediately Are these things to think about? Are these the things you want most? Well, your exact value Or if you care about the exact amount of money you are talking about Here, \$ 120 is a lot of money. So let me assume this is a huge amount of money. But it will be behind your mind. Well, I'll just take it later, but something I must have forgotten. And you may be right. You will miss out on opportunities If you only took your money with 10% security early. And if you want to compare them directly You may have thoughts.

Well, if I had taken option 1, I would have taken \$ 100 And if you put it in the bank What does a 10% security measure depend on? Well, after one year, 10% of \$ 100 is \$ 10. So you get \$ 10 worth of benefits. Saved in your bank after one year Now it will be \$ 110. It starts with a little practice We can now assume that we have actually paid \$ 100 You can keep 10% safe in the bank It will turn into \$ 110 in just one year Better than \$ 109 a year later. So this kind of situation or this kind of idea Or just having that choice You will do well. You lose one dollar a year What about two years from now? Well, at least you didn't go down without explaining yourself first That would be \$ 110. And 10% of the \$ 110 will be \$ 11 If you want to add \$ 11, that would be \$ 121. So next time you should take \$ 100 By investing annually in a 10% safe bank. It will come to \$ 121. this Someone insure you Better a poor horse than no horse at all. Next time you will lose one dollar. Therefore, the issue of quantity is no longer important. But if you get it, think like this This is called the time value of money.

Time value of money Or another way to think The point is, time is of the essence. Expected Benefits And by doing this you can compare your money. That will be equal to the amount of money next time. Think again about the value of time now Or another way of communicating with money, I think Is the current value of the current thought value. I'm probably talking about the future and the present. So present and future values ​​are future values.

Assuming 10% like this If someone asked you, what is the present value? What will happen to \$ 121 in the next two years? They should ask you. The question is, what is the current value? The present value is the present value. What is the current value of \$ 121 over the next two years? How much money is in line with what? Or how much money do you have in your bank? Is \$ 121 Safe for the Next 2 Years? We know you put \$ 100 in the bank You get \$ 121 for 2 years of free 10% security. So the current value here is The \$ 121 value is \$ 100. Or think of the present and the future differently What if someone asks you what the future holds? So what is the future value of this \$ 100 in a year? So the futures value in a year is from 110 If you get it from a bank that guarantees 10% security Two years later, the futures will be \$ 121. So let me give it to you Another interesting problem like this.

So let's just say I have ………… .. let's say If we have to think about it all the time A 10% free profit will make our numbers easier. And let's say someone said they were The idea is to give you \$ 65 a year. And if we have to ask ourselves again What is the current value of this? What is the current value of this? Do you remember the present value we asked you? The amount of money is for you Putting it in a free profitable bank Is that the equivalent of \$ 65? Are these two compatible for you? You say, "Well, no matter how much money." Let's just call it X. No matter how much money you have, time is of the essence If only the official increase of 10% I would assume it is X + 10% X +… .. Let me write this like this: Let me write + 10% xX…. Let me be clear and do this. X + 10% X should be equivalent to \$ 65. What if I take 10% of what I get? By the end of the year, it should be worth \$ 65. This is the same thing as 1X Or we can say 1X + 10%. 0.10X is equal to \$ 65 or the sum of these two.

If you want to calculate 1.1.X = 65 What is the true value of this present value? Divide both sides by 1.10 What does your X look like? Let me do it this way… It will be a little clearer. So let's say we divide one side by 1.0 And it doesn't matter if the numbers are followed by 0s We are not too worried about the accuracy of this Because that's really 10%. So this has to be discarded. And it will be equal to X. Let me give you a calculator. 65 divided by 1.1 equals X. The average is \$ 59.09. Therefore, X = 59.09 is the present value \$ 65 per year Or something else to think about If you want to know the value of the future 10% profit on \$ 59.09 per year You will receive \$ 65..