Rate Q&A: APY to APR and APR to APY conversion methods

APR and APY are common concepts of savings interest rate that you have to deal with.  For example, the review of online saving accounts lists APY version of various bank’s saving account interest rates.  The concepts of APR and APY are so close to each other, they sometimes confuse a lot of people.  In fact, they describe the same thing, interest rate, from two perspectives.  APR stands for Annual Percentage Return, it measures how much interest dollar you will get if you cash out whenever you earn interest.  APY stands for Annual Percentage Yield, it measures how much interest dollar you will get if you don’t cash out interest earned, but put it back to earn interest again.

The two types of rates are interchangable, here is how to convert one to the other.   Before you calculate, you need to set a method of compounding, which is how many pieces you want to slice a year into.  Daily compounding slices a year into 365 days, then periods of year is 365.  Monthly compounding slices a year into 12 months, then periods of year is 12.  With this in your mind, you can start converting.

Supposing you want to calculate daily rate for the year of 2009 which has 365 days total.

If you have APR available, here is how to calculate APY:

APY = (APR / periods of year + 1) ^ periods of year – 1

For example, for APR 2.08%, and you want daily APY,

APY = (2.08% / 365 + 1) ^ 365 – 1 = 2.10%

Converting APY to APR is a little more complicated, say If you have APY available, and need APR

APR = ((1 + APY) ^ (1/periods of year) – 1) * periods of year

For example, for APY 2.10%, and you want daily APR,

APR = ((1 + 2.1%) ^ (1/365) – 1) * 365 = 2.08%