Effective Annual Rate A loan is offered with monthly payments and a 6.5 percent APR. What's the loan's effective annual rate (EAR)?

Question

Quizplus · Accepted Answer

To calculate the annual percentage rate (APR) of a loan with monthly payments, we can use the following formula:

APR = (2 / n) * ((FV / PV)^(12/n) - 1)

Where:
n = number of payments per year (12 for monthly payments)
FV = future value of the loan
PV = present value of the loan

Plugging in the values given in the question, we get:

6.5% = (2/12) * ((FV / PV)^(12/12) - 1)

Solving for (FV / PV), we get:

(FV / PV) = (1 + 6.5%/2)^(12/2) = 1.06697

To find the effective annual rate (EAR), we need to convert the APR into the EAR using the following formula:

EAR = (1 + APR / n)^n - 1

Plugging in the values, we get:

EAR = (1 + 6.5%/12)^12 - 1 = 6.697%

Therefore, the answer is B.

Effective Annual Rate a Loan Is Offered with Monthly Payments