How to Calculate Annual Equivalent Rate

by Michael Keenan
The more often interest compounds, the higher the annual equivalent rate.

Though banks give you an annual interest rate, it's usually slightly misleading because it doesn't account for interest compounding. Each time that interest gets added to your account, that's more money to earn interest for the remainder of the year. For example, if you earn $5 of interest in January, that $5 accrues additional interest for the remaining 11 months of the year. The annual equivalent rate measures the actual rate of return you get after including the effects of interest compounding. To figure the annual equivalent rate, you need to know the stated rate and how many times per year interest compounds.

Convert the stated interest rate to a decimal by dividing by 100. For example, if a savings account offers you 3 percent interest, divide 3 by 100 to get 0.03.

Divide the stated interest rate as a decimal by the number of times interest is paid per year. For this example, if the saving account pays interest monthly, divide 0.03 by 12 to get 0.0025.

Add 1 to the result. Continuing the example, add 1 to 0.0025 to get 1.0025.

Raise the result to the power of the number of times interest is added each year. In this example, raise 1.0025 to the 12th power to get 1.030415957. On a calculator, the power key is usually represented by a "^" or "x^y."

Subtract 1 and multiply the result by 100 to find the annual equivalent rate. Finishing this example, subtract 1 from 1.030415957 to get 0.0304 and multiply by 100 to get 3.04 percent. This is your annual equivalent rate.

About the Author

Mark Kennan is a writer based in the Kansas City area, specializing in personal finance and business topics. He has been writing since 2009 and has been published by "Quicken," "TurboTax," and "The Motley Fool."

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