Elizabeth opened a credit card at a department store with an APR of 17.71% compounded quarterly. What is the APY on this credit card?
First off, let's talk APR and APY. The APR is the annual rate of interest - it doesn't take the compounding into account. The APY is also the annual rate of interest but does take the compounding into account.
So one way to find the APY is to run through a calculation with compounding. Since there are only four quarters to compound through, I'll do it the "long way" and won't use a standard formula.
For our example, let's say that at the start of the year, we buy $100 of stuff.
At the end of Q1, we owe a quarter's worth of interest:
At the end of Q2:
At the end of Q3:
And at the end of Q4:
The APY, therefore, is roughly