How to Convert Annual Interest Rate to Quarterly Interest

by Michael Keenan ; Updated July 27, 2017

Annual interest rates can be expressed as either an annual interest rate or an annual percentage yield. To convert an annual interest rate to the quarterly rate, you can simply divide by four. For example, an annual percentage rate of 8 percent would equate to a quarterly rate of 2 percent. However, if you have the annual percentage yield, which takes into account interest compounding, you must perform a more complex calculation.

Step 1

Divide the annual percentage yield by 100 to convert it to a decimal. For example, if the annual percentage yield equals 8.05 percent, you would divide 8.05 by 100 to get 0.0805.

Step 2

Add 1 to the result from step 1. In this example, you would add 1 to 0.0805 to get 1.0805.

Step 3

Raise the result from step 1 to the 0.25th power, since interest compounds four times per year. In this example, you would raise 1.0805 to the 0.25th power to get 1.019544516.

Step 4

Subtract 1 from the result from step 3 to find the quarterly interest rate expressed as a decimal. In this example, you would subtract 1 from 1.019544516 to get 0.019544516.

Step 5

Multiply the result from step 4 by 100 to convert the quarterly interest rate expressed as a decimal expressed as a percentage. Finishing the example, you would multiply 0.019544516 by 100 to get about 1.95 percent per quarter.

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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