APR to APY Calculator

Calculate the annual percentage yield given an annual percentage rate using the APR to APY calculator below.

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Annual Percentage Yield:

APY:
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Learn how we calculated this below

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By
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Joseph Rich holds a Master's degree in finance and a Bachelor's degree in economics. He specializes in economics and investing analysis.

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Reviewed by
Bio image of Laura Deimling, MBA

Laura started her career in Finance a decade ago and provides strategic financial management consulting. She has an MBA in Finance and a Bachelor's in Economics.

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How to Convert APR to APY

APR stands for annual percentage rate. The APR interest rate is the simple interest rate plus other fees that the bank may charge you, such as financing fees and prepaid fees. It represents the true cost of borrowing if the loan is a simple interest loan.

APY stands for annual percentage yield. APY is the interest rate that is calculated once compounding is taken into consideration. Since this is a compounding interest rate, the more frequent the compounding, the higher the total interest will be.

APR and APY are similar in that they both annualize the interest rate (and why they both have “annual” in their names), but differ in several ways:

The APY takes compounding into effect, but the APR does not. So the APR more accurately represents the cost of borrowing on a loan because most loans use simple interest. The APY more accurately represents what the return on investment is for a savings account because the bank will pay you compound interest (interest on the principal balance and previously accrued interest).

The APR includes other additional fees that the financial institution may charge on top of the interest rate, whereas the APY only includes the interest rate.

APR to APY Formula

If you already know the APR, you can use the APR to APY formula, which is the formula that the calculator above uses. This formula is as follows:

APY = \left (1 + \frac{APR}{m} \right)^{m} − 1

Where:
APY = annual percentage yield
APR = annual percentage rate
m = compounding periods

For example, let’s say your loan has an APR of 12.7% compounded quarterly (m = 4). What would your APY be on this loan?

APY = \left (1 + \frac{12.7\%}{4} \right)^{4} − 1
APY = \left (1 + 3.175\% \right)^{4} − 1
APY = 1.133177 − 1
APY = 13.3177\%

Would the APY change at all if instead the interest rate was compounded daily (m = 365)?

APY = \left (1 + \frac{12.7\%}{365} \right)^{365} − 1
APY = \left (1 + .0348\% \right)^{365} − 1
APY = 1.135392 − 1
APY = 13.5392\%

We can see that the more frequent the compounding in a year, the higher the APY will be.

How to Convert APY to APR

By reversing the process above you can also convert an APY back to an APR.

APY to APR Formula

Given the APY you can use the following formula to calculate the APR:

APR = \left [ \left (APY + 1\right )^{ \frac{1}{m} } − 1 \right ] \times m

Where:
APR = annual percentage rate
APY = annual percentage yield
m = compounding periods

For example, assume we have a loan with an APY of 15.5% compounded weekly (m = 52). What would be the APR of this loan?

APR = \left [ \left (15.5\% + 1\right )^{ \frac{1}{52} } − 1 \right ] \times 52
APR = \left [ 1.155^{ 0.019231 } − 1 \right ] \times 52
APR = \left [ 1.002775 − 1 \right ] \times 52
APR = 14.43\%

Now, instead of weekly compounding, what if the APY was compounded semiannually (m = 2)?

APR = \left [ \left (15.5\% + 1\right )^{ \frac{1}{2} } − 1 \right ] \times 2
APR = \left [ 1.155^{ 0.5 } − 1 \right ] \times 2
APR = \left [ 1.074709 − 1 \right ] \times 2
APR = 14.94\%

When we go from the APY to APR, the more frequent the compounding, the lower the rate–the opposite of what we saw with the APR to APY conversion.

This is due to the compounding of the APY. The more times an interest rate is compounded per year, the higher its compounded interest rate will be relative to the simple interest rate. This shows that the more times interest is compounded per year, the farther the simple and compound interest rate move from each other.

If we hold the compound rate constant and increase the frequency of compounding, the simple interest rate must fall.

But if we hold the simple interest rate constant and increase the frequency of compounding, the compound interest rate must increase. You can learn more about this concept on our interest rate calculator, which shows the difference between compound and simple interest rates.

You might also be interested in our EAR calculator to find the effective annual rate.

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