What is compound interest

Supposing you pay 12% interest per year on a loan of, let's say, $1000. If you make no payments, then at the end of the year the bank would charge $120 in interest, giving a balance of $1120.

However, most banks will compound the interest - that is, apply a portion of the interest several times over the year. By compounding the interest, they can charge interest ON THE INTEREST.

For example, if the interest is 12% per year, but is compounded monthly, then the bank would charge 1% per month. Assuming again that no payments are made, at the end of the month you would be charged $10, for a balance of $1010.

HOWEVER, at the end of the second month, the bank would again charge 1%, but THIS TIME it would be on the $1010, not the original $1000. You would be charged $10.10 in interest, giving a balance of $1020.10

At the end of the year, the balance would be $1126.83, which is more than the balance if the interest had not been compounded. Banks will call this the Annual Percentage YIELD (APY) which tells you the yearly interest accrued due to compounding. The annual percentage rate is 12%, but the APY is actually 12.683%.

There is a formula that shows how interest is accrued when compounded:
A = Balance at the end of the term
P = Principal
r = interest rate as a decimal
n = number of times compounded per year
t = number of years

The formula is A = P·(1 + r/n)^(nt)

In my example, P = 1000, r = 0.12, n = 12, t = 1
So A = 1000(1 + .12/12)^(12·1) = 1126.83