What is compound interest

for my gcse mock exam, i had a question about compound interest.
what is it?
and also , if someone has a certain amount of money after 3 years of compound interest, how do you work out how much interest they've earned each year? my maths teacher said it was something to do with powers..
hrm.
hope you geniuses can help me ;D
x

Suppose that you have 100 dollars and you want to invest it in something for a specified amount of interest. There are 2 types of interest that you can get: simple or compound.

Now, if you invest it in simple interest, the interest that is gained is gained on the original principal. So, supposing that you get 5% per year for 10 years, you'll get, overall, 50% of your original amount as interest:

100 * (1 + (5/100) * 10) =>
100 * (1 + (5/10)) =>
100 * (15/10) =>
10 * 15 =>
150

The general formula for this would be: A = P * (1 + (i * t))

A = final amount
P = principal
i = interest rate
t = time

Compound interest works slightly differently. With compound interest, interest it paid upon whatever the existing amount is. For instance, let's say that we have the same scenario as before:

P = 100
i = 5%
t = 10 years.

How much will you have after 1 year?

100 * (1 + (5/100)) =>
100 * (105/100) =>
105

In the second year, you add 5% to the 105 dollars:

105 * (105/100) =>
21 * 21 / 4 =>
441 / 4 = >
110.25

Now, with simple interest, you'll only have 110 dollars after 2 years.

Third year: 110.25 * 105/100 => 115.7625
And so on and so forth. The general formula for compound interest is:

A = P * (1 + i)^t

P = 100
i = 5%
t = 10

A = 100 * (1.05)^10
A = 162.889462677744140625

Compound interest is exactly what it says on the tin: It is interest that is compounded upon interest over and over again

Simple interest on a deposit is where you get a percentage of the original deposit.