Compound interest on a deposit, loan or investment takes into account any interest that has already accumulated--as opposed to simple interest, which is concerned only with the initial principal. Given time, compound interest will accumulate much faster than simple interest, as the amount of interest received at the end of each payment period is always rising.

## Interest

Simple interest is calculated at the end of each period as a percentage of the principal--the initial amount of the loan or investment. A deposit of $1,000 with 5 percent simple interest monthly would thus accrue $50 each month, regardless of how long the funds are held.

## Compound Interest

Compound interest calculates interest not as a percentage of the principal but as a percentage of the principal plus the interest that has already accumulated. In the above example, the $1,000 account would accumulate $50 the first month, $52.50--5 percent of $1,050--the second month, $55.12 the third month, and so on.

## Compound Interest Formula

The standard formula for computing compound interest is:

P * (1 + r)^n = M

where M is the amount of money you end up with, P is the principal, r is the interest rate expressed as a decimal, and n is the number of periods. If you were to run the above example for three months, the formula would be:

1,000 * (1 + .05)^3 = 1,157.62

## Usefulness

Obviously, compound interest adds up much faster than simple interest--plus, its speed increases as time passes and the amount of money increases. The interest your bank pays you for the amount of money in your account is compounded: the more money you have, the more you make.

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