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How to Convert a Rate to APY

In applications or advertisements for credit cards, you’ve most likely seen interest rates shown as the Annual Percentage Rate (APR) and Annual Percentage Yield (APY). The difference between the two rates is that APR doesn’t take the compounding of interest into account while APY does.

There may be times when you will only be given the APR, so knowing how to convert the APR to an APY can come in handy. In our example, interest will be quarterly, and the rate will be 5 percent.

How to Convert a Rate to APY


Things You’ll Need

  • Calculator


5 Steps to Convert a Rate to APY

1. Determine the periodic rate by dividing the APR by the number of times that the interest is compounded annually.

Periodic rate = APR / number of periods

Periodic rate = .05 / 4 = .0125

Remember, since the 5 percent APR is a percentage, you need to convert it to decimal form before plugging it into the formula. The number of periods is 4 since the interest is being compounded quarterly.

2. Add 1 to the periodic rate (.0125) to get 1.0125.

3. Multiply 1.0125 exponentially by 4, so you’ll be multiplying 1.0125 by itself 4 times. The product would be 1.0509453369140625.

4. Subtract 1 from 1.0509453369140625 to get .0509453369140625.

5. Convert the decimal at the end of Step 4 back into a percentage by multiplying it by 100 and rounding to two decimal points. The APY is 5.10 percent.


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