What is the annual percentage yield (or effective annual rate) for a nominal rate of 7.5% compounded quarterly? Round your answer to two decimal places.
A)10.38%
B)6.14%
C)8.01%
D)7.71%
E)9.11%

Question

What is the annual percentage yield (or effective annual rate) for a nominal rate of 7.5% compounded quarterly? Round your answer to two decimal places. ​
A)10.38%
B)6.14%
C)8.01%
D)7.71%
E)9.11%

Quizplus · Accepted Answer

The annual percentage yield (APY) or effective annual rate can be calculated using the formula: $$APY = (1 + \frac{r}{n})^n - 1$$ where $r$ is the nominal annual interest rate (expressed as a decimal), and $n$ is the number of compounding periods per year. For a nominal rate of 7.5% (or 0.075 as a decimal) compounded quarterly ($n = 4$), the calculation is: $$APY = (1 + \frac{0.075}{4})^4 - 1 = (1 + 0.01875)^4 - 1 \approx 0.0771$$ or 7.71% when converted to a percentage and rounded to two decimal places.

What Is the Annual Percentage Yield (Or Effective Annual Rate)