APR and APY

CFA Level I
#1

Hello Guys,

Can anyone explain me in greater detail about the APR (Annual Percentage Rate) and APY (Annual Percentage Yield) w.r.t the bleow problem.

A bank quotes Certificate of Deposit (CD) yields both as annual percentage rate without compounding and as annual percentage yield (APY) that include the effects of monthly compounding. A $100,000 CD will pay $110,471.31 at the end of the year. Find the APR and APY the bank is quoting.

Thanks in Advance.

Deepak

#2

The question itself answered your first question. The difference between APR and APY is that APR does not consider compounding while APY does consider compounding. And so APY will never be smaller than APR.

For the problem: APY = (1 + HPY) ^ (365 / t) - 1

APY = (1 + ($10,471.31 / $100,000)) ^ (365 / 365) - 1 = 10.47% (t = 365 days here because it was valued at end of the year)

Number of compounding periods is monthly so 12 for this example.

We know that APY = (1 + (APR / # of compounding periods) ^ # of compounding periods - 1

So 10.47% = (1 + (APR / 12)) ^ 12 - 1

This is how I personally move this around step by step to determine APR:

10.47% + 1 = (1 + (APR / 12)) ^ 12

1.1047 ^ (1 / 12) = 1 + (APR / 12)

1.0083 -1 = APR / 12

0.0083 * 12 = APR

APR = 10.0%