Calculate the Effective Annual Rate of a Loan

What is the effective annual rate (EAR) of a loan with a stated annual percentage rate (APR) of 6% compounded monthly?

A. 8.02%

B. 7.4%

C. 6.17%

D. 6.78%

Answer:

The effective annual rate (EAR) for a loan with an APR of 6% compounded monthly is closest to C. 6.17%.

Calculating the effective annual rate (EAR) of a loan with a stated annual percentage rate (APR) of 6% compounded monthly involves using the formula EAR = (1 + APR/n)^n - 1.

Given that the APR is 6% or 0.06 and the compounding frequency is monthly, we can substitute these values into the formula:

EAR = (1 + 0.06/12)^12 - 1

By simplifying this calculation, we get:

EAR = (1 + 0.005)^12 - 1

EAR = 1.061678 - 1

EAR ≈ 0.061678 or 6.17%

Therefore, the effective annual rate (EAR) for the loan is approximately 6.17%, making option C the closest answer.