Main content

### Course: Finance and capital markets > Unit 1

Lesson 1: Compound interest basics# Compound interest introduction

Learn about the basics of compound interest, with examples of basic compound interest calculations. Created by Sal Khan.

## Want to join the conversation?

- So you are telling me that in the USA they pay you to keep your money in the bank ? why isn't everyone depositing huge ammounts into banks then ?(122 votes)
- Most savings accounts don't pay anywhere near enough interest to keep up with inflation. There are a few that might, but most do not. Right now Chase pays .01% for a savings account. Most of the money that banks lend is borrowed from the federal government at a lower rate and then they lend it to you at a higher rate. That is why rates go up and down when the fed changes rates.(82 votes)

- does the U.S. treasury continously compound interest?(68 votes)
- The U.S. treasury is a zero-coupon debt security that is bought at the market value(e.g. $99) lower than its face value(e.g. $100), with the face value repaid at the time of maturity (depends if it is a bill, a note, or a bond). The interest (return on capital) is a predetermined rent of the lending.(26 votes)

- why does the bank pay you?

not you pay the bank?(18 votes)- When you deposit money with a bank, the bank pays you interest. When you take a loan from the bank, you pay the bank interest. The one who pays interest is the one who gets the other person's money.(36 votes)

- 0:31; 10 percent interest that compounds annually? Is it okay if I put my money in your bank?(19 votes)
- What's the difference between a loan and an interest?(5 votes)
- A loan is how much you borrow, and interest is basically the price you pay for the right to borrow money.

Suppose you borrow $100 from a friend. They say, no problem! Pay me back next week. Next week you pay your friend back $100. No interest is paid to your friend.

But if you go to a bank, the bank will say "Sure! But we charge 10% interest". A week later you pay back the $100 loan you borrowed (which is sometimes called the "principle" of a loan), plus $10 in interest.(18 votes)

- Does interest rate change government budget(8 votes)
- Yes. If the cost of the government's current debt is too high, the government is less likely to spend more money.(9 votes)

- Can the Treasury raise intrest at their will,or does it go wuth the ecomnmy?

-Aaron J(12 votes)- In the U.S. it's the Federal Reserve System that raises & lowers the Prime Lending Rate. This done by buying U.S Treasury Securities (bonds, bills & notes), which drives the interest rates that all other lenders charge.(1 vote)

- Which is considered better simple or compound interest?(5 votes)
- If both rates are the same (lets say 8%) and you are borrowing money, then simple interest would be to your advantage. Compound interest would accrue much faster and you would have to pay more money back. If you are lending money, then by charging compound interest you would make more money.(9 votes)

- Fun not fun fact: Most of the trustable and secured banks compounds rate are extremely low. You'll need to really pour a very large amount of money in order to see it worth it.

Keep on mastering the art of money management fellows :)

#GoKhanAcademy(8 votes) - would the bank ever stop paying us? what if we keep all our money into a bank for the rest of our lifes(4 votes)
- No, as long as you keep your money in the bank you will get paid a certain percentage, unless in certain cases where the bank collapses/ goes bankrupt. You can keep all your money in the bank, but we know for every input there is always an output, unless you're assuming you're not going to spend on daily necessities which is basically impossible.(6 votes)

## Video transcript

Male Voice: What I want
to do in this video is talk a little bit
about compounding interest and then have a little bit of a discussion of a way to quickly, kind
of an approximate way, to figure out how quickly
something compounds. Then we'll actually see how good of an approximation this really is. Just as a review, let's say I'm running some type of a bank and I tell you that I am offering 10% interest
that compounds annually. That's usually not the
case in a real bank; you would probably compound continuously, but I'm just going to
keep it a simple example, compounding annually.
There are other videos on compounding continuously.
This makes the math a little simpler. All that
means is that let's say today you deposit $100
in that bank account. If we wait one year,
and you just keep that in the bank account, then
you'll have your $100 plus 10% on your $100 deposit. 10% of 100 is going to be another $10. After a year you're going to have $110. You can just say I added 10% to the 100. After two years, or a year
after that first year, after two years, you're going to get 10% not just on the $100,
you're going to get 10% on the $110. 10% on 110 is you're going to get another $11, so 10% on 110 is $11, so you're going to get 110 ... That was, you can imagine,
your deposit entering your second year, then
you get plus 10% on that, not 10% on your initial deposit. That's why we say it compounds. You get interest on the
interest from previous years. So 110 plus now $11. Every year the amount of interest we're getting, if
we don't withdraw anything, goes up. Now we have $121. I could just keep doing
that. The general way to figure out how much you
have after let's say n years is you multiply it. I'll use
a little bit of algebra here. Let's say this is my original
deposit, or my principle, however you want to
view it. After x years, so after one year you
would just multiply it ... To get to this number right
here you multiply it by 1.1. Actually, let me do it this way. I don't want to be too abstract. Just to get the math here,
to get to this number right here, we just multiplied that number right there is 100 times 1
plus 10%, or you could say 1.1. This number right here is going to be, this 110 times 1.1 again.
It's this, it's the 100 times 1.1 which was
this number right there. Now we're going to multiply
that times 1.1 again. Remember, where does the 1.1 come from? 1.1 is the same thing as
100% plus another 10%. That's what we're getting.
We have 100% of our original deposit plus another 10%, so we're multiplying by 1.1. Here, we're doing that twice. We multiply it by 1.1 twice. After three years, how
much money do we have? It's going to be, after
three years, we're going to have 100 times 1.1 to the
3rd power, after n years. We're getting a little abstract here. We're going to have 100
times 1.1 to the nth power. You can imagine this is
not easy to calculate. This was all the situation
where we're dealing with 10%. If we were dealing in a
world with let's say it's 7%. Let's say this is a
different reality here. We have 7% compounding annual interest. Then after one year we
would have 100 times, instead of 1.1, it would be 100% plus 7%, or 1.07. Let's go to 3 years. After 3 years, I could do 2 in between, it would be 100 times
1.07 to the 3rd power, or 1.07 times itself
3 times. After n years it would be 1.07 to the nth power. I think you get the
sense here that although the idea's reasonably
simple, to actually calculate compounding interest is
actually pretty difficult. Even more, let's say I were to ask you how long does it take
to double your money? If you were to just use
this math right here, you'd have to say, gee, to double my money I would have to start with
$100. I'm going to multiply that times, let's say whatever, let's say it's a 10% interest, 1.1
or 1.10 depending on how you want to view it, to
the x is equal to ... Well, I'm going to double my money so it's going to have to equal to $200. Now I'm going to have to solve for x and I'm going to have to
do some logarithms here. You can divide both sides by 100. You get 1.1 to the x is equal to 2. I just divided both sides by 100. Then you could take the
logarithm of both sides base 1.1, and you get x. I'm showing you that this is complicated on purpose. I know this is confusing. There's multiple videos on how to solve these. You get x is equal to log base 1.1 of 2. Most of us cannot do this in our heads. Although the idea's simple, how long will it take for me to double
my money, to actually solve it to get the exact answer, is not an easy thing to do. You
can just keep, if you have a simple calculator, you
can keep incrementing the number of years until you
get a number that's close, but no straightforward way to do it. This is with 10%. If
we're doing it with 9.3%, it just becomes even more difficult. What I'm going to do in the next video is I'm going to explain something called the Rule of 72, which
is an approximate way to figure out how long,
to answer this question, how long does it take
to double your money? We'll see how good of
an approximation it is in that next video.