What Is Compound Interest Rate?

Compound interest arises when interest is added to the principal, so that from that moment on, the interest that has been added also itself earns interest. This addition of interest to the principal is called compounding.

A bank account, for example, may have its interest compounded every year: in this case, an account with $1000 initial principal and 20% interest per year would have a balance of $1200 at the end of the first year, $1440 at the end of the second year, and so on.

In order to define an interest rate fully, and enable one to compare it with other interest rates, the interest rate and the compounding frequency must be disclosed.

Since most people prefer to think of rates as a yearly percentage, many governments require financial institutions to disclose the equivalent yearly compounded interest rate on deposits or advances. For instance the yearly rate for a loan with 1% interest per month is approximately 12.68% per annum (1.01^12).

This equivalent yearly rate may be referred to as annual percentage rate (APR), annual equivalent rate (AER), annual percentage yield, effective interest rate, effective annual rate, and by other terms. When a fee is charged up front to obtain a loan, APR usually counts that cost as well as the compound interest in converting to the equivalent rate. These government requirements assist consumers to compare the actual costs of borrowing more easily.

For any given interest rate and compounding frequency, an "equivalent" rate for any different compounding frequency exists.

Compound interest is calculated each period on the original principal  and all  interest accumulated during past periods.  Although the interest may be stated as a yearly rate, the compounding periods can be yearly, semiannually, quarterly, or even continuously.

You can think of compound interest as a series of back-to-back simple interest contracts. The interest earned in each period  is added to the principal of the previous period to become the principal for the next period.  For example, you borrow $10,000 for three years at 5% annual interest compounded annually:

interest year 1 = p * i * n = 10,000 * .05 * 1 = 500
interest year 2 =  (p2 = p1 + i1) * i * n = (10,000 + 500) * .05 * 1 = 525
interest year 3 = (p3 = p2 + i2) * i * n = (10,500 + 525) *.05 * 1 = 551.25

Total interest earned over the three years  = 500 + 525 + 551.25 = 1,576.25.   Compare this to 1,500 earned over the same number of years using simple interest.