APR and APY, what is the difference

A question from notes SS.2 TVM: A bank quotes certificate of deposit (CD) yields both as annual percentage rates (APR) without compounding and as annual percentage yields (APR) that include the effects of monthly compounding. A $100,000 CD will pay $100, 471.31 at the end of the year. Calculate the APR and APY the bank is quoting.

Wolwol, I’m not sure what your purpose for posting this question is, but I’ll share with you how I would look at the problem. First, APR is convienent way for banks to state the periodic interest rate as an annual rate. On pg. 179 of vol. 1 of the level 1 CFA cirriculm, an example is given where a bank pays interest on a monthly basis for a cd. This monthly rate is multiplied by 12 as follows: (1+periodic rate)*12 to show the APR. This rate is meaningless as a measure of investment return because it ignores compounding. Therefore, investor must calculate APR which shows the effects of compounding and is a way to measure effective rate of return. The formula for APY is shown on pg. 182 as (1+periodic rate)^periods per year. In the problem you posted, we are given the beginging investment value and the ending investement value. In addition we are told that interest is compounded monthly for one year. With these facts, we can find both APR and APY. Note that the ending value consists of the begining investment value + interest payments + interest earned on interest payments. In order to find the periodic (in this case monthly) rate we do the following: 1. subtract beginging invest value from the ending value to show the interest value 100,471.31 - 100,000 = 471.31 (because the initial investment value is a round number we can see that the the APY is .47131%, however this is not always so obivious.) 2. Divide the interst value by the beginging investment value to show the rate of return: 471.31/100,000 = .0047131 3. raise the rate of return plus one to the inverse power of the number of periods per year and then subtract one to show the periodic interest rate. (1+.0047131)^1/12 = 1.00039191 - 1 = .00039191 4. mutiply the periodic rate by periods per year to show the APR: 00039191 * 12 = .00470292 or .470292% You can see that the APR will always be less than the APY unless the inerest is compounded annually in which case they would be the same. However, the APR should be close to the APY and I often do a sanity check to make sure that the two rates make sense. For example if I calculate the APY as 8.3% and the APR as 4.15% I know I have made a mistake somewhere.

3x a lot, los I do not have the curriculum now, the notes do not have the clear-cut concepts of APR and APY.