Compound interest occurs when a person earns or an institution charges interest on top of previously accrued interest. For example, if an investor has a savings account that earns $100 in September in addition to his deposit, the bank will also pay interest on the $100 of earned interest. The formula for compound interest is one plus the interest rate per compounding period raised to the power of the number of times the deposit compounds. Multiplying this formula by any amount will provide the compound interest earned on the amount.
Determine the amount of money earning interest, the interest rate and the amount of time the money will earn interest. For example, a person deposits $500 in a bank for a year and a half. The money earns 9 percent interest per year. The account compounds monthly.
Divide the interest by the amount of times the account compounds annually to determine the interest rate per compounding period. In the example, 9 percent divided by 12 months equals 0.0075.
Add one to the interest rate per compounding period. In the example, 0.0075 plus 1 equals 1.0075.
Multiply the number of times the account compounds per year by the number of years it compounds. In the example, 1.5 years times 12 months equals 18.
Raise the number calculated in Step 3 by the number calculated in Step 4. In the example, 1.0075 raised to the power of 18 equals 1.143960389. This is the compound interest factor.
Multiply the amount of money compounded by the compound interest factor. In the example, $500 times 1.143960389 equals $571.99. This is the total amount due.
Subtract the amount of money compounded by the total amount due to calculate the compound interest payment. In the example, $571.99 minus $500 equals $71.99 due in compound interest.