Question

Ben opened a credit card at a department store with an APR of 27.99% compounded monthly. What is the APY on this credit card?

Answer 1

APR is the monthly interest rate multiplied by 12 to give consumers an idea of the interest rate. It is close to the real (compound) rate if the rate is low, but makes a big difference if the interest is high, as in the present case.
APY is calculated by
r=APR/12
APY=(1+r)^12 -1

You will find that in the current case, APY is almost 1/7 higher than APR.

Also, see explanation below.
http://www.investopedia.com/articles/basics/04/102904.asp#axzz25jOp8We5

Defining APR and APY
APR is the annual rate of interest without taking into account the compounding of interest within that year. Alternatively, APY does take into account the effects of intra-year compounding. This seemingly subtle difference can have important implications for investors and borrowers. Here is a look at the formulas for each method:


For example, a credit card company might charge 1% interest each month; therefore, the APR would equal 12% (1% x 12 months = 12%). This differs from APY, which takes into account compound interest. The APY for a 1% rate of interest compounded monthly would be 12.68% [(1 + 0.01)^12 – 1= 12.68%] a year. If you only carry a balance on your credit card for one month's period you will be charged the equivalent yearly rate of 12%. However, if you carry that balance for the year, your effective interest rate becomes 12.68% as a result of compounding each month.

So if he has an APR of 27.99%, the monthly interest (i.e. per period) is r=27.99/12.
Over a year, with a fixed amount outstanding, he would have an APY (i.e. interest compounded over a year) of APY=(1+r)^12, almost 14% more than APR.

Answer 2

From @mathmate's instruction, use effective interest rate formula to calculate
APY = ( 1+ APR/12 ) ^12 - 1

with APR = .2799
@ChristiLynn13 Give us feedback see if you can come up with the answer.