Final answer:
The effective annual rate (EAR) for a loan with an APR of 6% compounded monthly is calculated using the formula EAR = (1 + APR/n)^n - 1, which gives an EAR of approximately 6.17%. Therefore, the closest answer is C. 6.17%.
Step-by-step explanation:
The question asks for the effective annual rate (EAR) of a loan with a stated annual percentage rate (APR) of 6% compounded monthly. The EAR can be calculated using the formula EAR = (1 + APR/n)n - 1, where n is the number of compounding periods per year. In this case, the APR is 6% or 0.06, and the compounding frequency is monthly, so n equals 12. Applying the values to the formula, we get EAR = (1 + 0.06/12)12 - 1.
Calculating the provided formula gives an EAR which can be approximated as:
EAR = (1 + 0.005)12 - 1
EAR = 1.061678 - 1
EAR = 0.061678 or 6.17%
Thus, the closest answer is C. 6.17%.