What method would you use to calculate the annual percentage yield (APY) for a quoted interest rate?

To calculate the annual percentage yield (APY) for a quoted interest rate, it's essential to factor in the effect of compounding, which is typically done on an annual basis. The context of the options suggests a scenario where a calculated method needs to be employed, specifically with a 7% interest rate and a specified number of periods (12 in this case indicates monthly compounding).

Using the formula that incorporates periodic compounding— along with the quoted rate— allows for the calculation of the total interest earned over the year considering the frequency of compounding. In this case, if the interest is compounded monthly, the formula for APY becomes:

[ \text{APY} = \left(1 + \frac{r}{n}\right)^{nt} - 1 ]

where ( r ) is the annual interest rate, ( n ) is the number of compounding periods per year, and ( t ) is the number of years. With a 7% interest rate and monthly compounding, this formula helps derive a more accurate measure of the yield, reflecting the compounding effect effectively.

In contrast, simply using the interest rate without any calculations would ignore the impact of compounding frequency and would not yield accurate