Lesson #2: APR vs APY

The second Financial Place Online lesson continues from the last lesson. For more than one period, the interest earned in the last period earns interest itself in the next period. That is why there is the time exponent in the formula. Each period that passes results in (1+i) times more money that was had at the start of that period. This is called compounding.

APR is the annual percentage rate. This is what banks and lenders typically quote for their rates. In this case the period may be any term up to a year. The APR is expressed as the interest rate per period times the number of periods in a year. For example a 0.5% monthly rate would result in a 6% APR. Likewise, a 6% annual rate would result in the same 6% APR.

APY is the annual percentage yield. This is similar to APR, but takes into account the compounding mentioned above. A 0.5% monthly rate (6% APR) would have an APY of [(1+0.005)^12]-1 = 6.17%. However, a 6% yearly rate (6% APR) would have an APY of [(1+0.06)^1]-1 = 6% since there is only one compounding period. In the monthly case there are 12 compounding periods within the year.

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