# 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?

18.93%

#### Explanation:

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: $100xx(17.71%)/4=$4.4275, which means we now owe$104.43 (rounded).

At the end of Q2:

$104.4275xx(17.71%)/4~=$4.6235, which means we now owe $109.05 (rounded). At the end of Q3: $109.051xx(17.71%)/4~=$4.8282, which means we now owe$113.88 (rounded).

And at the end of Q4:

$113.8792xx(17.71%)/4~=$5.0420, which means we now owe \$118.93 (rounded).

The APY, therefore, is roughly 18.93%. Note that the quarterly compounding changed our 17.71% APR into being more than 1% higher.