The annual percentage rate measures the amount of interest an investment earns over the course of a year. When interest is compounded, investments grow faster because the new interest earned each period includes the principal investment, plus the previous periods' interest. This is unlike simple interest, which applies only to the principal amount. Depending on the investment, interest can be compounded annually, quarterly, monthly or daily. The annual percentage rate formula is (1 + i ÷ m)^m – 1.0. Although it may seem intimating, figuring the APR is a relatively simple task.
Divide the interest rate by 100 to convert it to a decimal. For instance, 5 percent becomes 0.05.Step 2
Divide the decimal-form interest rate by the number of times the interest compounds each year. For instance, for an investment at 5 percent that compounds interest quarterly, divide 0.05 by 4 to get 0.0125.Step 3
Add 1 to the resulting figure to turn it into a whole number. For instance, 0.0125 becomes 1.0125.Step 4
Raise the answer to the mth power, with "m" representing the number of times the interest compounds each year. As an example, 1.0125 to the fourth power is 1.051.Step 5
Subtract 1 from the figure to turn it back into a decimal. For instance, 1.051 becomes 0.051.Step 6
Multiply the decimal by 100 to convert it to a percentage. As an example, 0.051 becomes 5.1 percent. This is the APR.
- As a rule, the annual percentage rate is only slightly higher than the actual interest rate.
Lauren Treadwell studied finance at Western Governors University and is an associate of the National Association of Personal Financial Advisors. Treadwell provides content to a number of prominent organizations, including Wise Bread, FindLaw and Discover Financial. As a high school student, she offered financial literacy lessons to fellow students.