The Difference Between Annual Percentage Rate (APR) and Annual Percentage Yield (APY) Explained

by Vinaya HS

Quite a number of readers had written in asking me to explain the difference between APR and APY.

APR = Annual Percentage Rate. Think of this as simple interest.

APY = Annual Percentage Yield. Think of this as compound interest.

APR and APY explain why your Fixed Deposit certificate quotes an interest rate of 9% but upon maturity you get an interest amount that is slightly higher than what you’d actually get at 9%.

APY = APR compounded at a certain compounding interval.

The exact formula that relates these two is:

APY = (((1 + (Quoted_APR/100)/Compounding_Interval)^Compounding_Interval) – 1)*100

Look at this illustration (click on the image for a full-size version).

GEO_Blog_APR_APY_Illustration

When APR = 10.25% and compounding is done quarterly then,

APY = (((1 + (10.25/100)/4)^4) – 1)*100 = 10.65%

On the other hand, if APR = 10.50% and compounding is done quarterly then,

APY = (((1 + (10.50/100)/4)^4) – 1)*100 = 10.92%

Finally, if APR = 10.25% and compounding is done semi-annually then,

APY = (((1 + (10.25/100)/2)^2) – 1)*100 = 10.51%

That explains the difference between APR and APY. Let me know if you have any questions.