What is the annual percentage yield (or effective annual rate) for a nominal rate of 8% compounded quarterly? Round your answer to two decimal places.
A) 11.1%
B) 6.56%
C) 8.54%
D) 8.24%
E) 9.64%

Question

What is the annual percentage yield (or effective annual rate) for a nominal rate of 8% compounded quarterly? Round your answer to two decimal places. ​
A) 11.1%
B) 6.56%
C) 8.54%
D) 8.24%
E) 9.64%

Quizplus · Accepted Answer

To find the annual percentage yield, we use the formula A = P (1 + r/n)^nt, where A is the end amount, P is the principal, r is the nominal interest rate, n is the number of times interest is compounded, and t is the time in years. Plugging in the given values, we get:

A = P (1 + 0.08/4)^(4*1)
A = P (1 + 0.02)^4
A = P (1.02)^4

To find the annual percentage yield, we solve for r in the formula A = P (1 + r)^t:

1.08 = (1 + r)^1
1.08^(1/4) = 1 + r
r = 1.0224 - 1
r = 0.0224

Converting the decimal to a percentage, the annual percentage yield is 2.24%. Rounded to two decimal places, the answer is D (8.24%).

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