Suppose Community Bank offers to lend you $20,000 for one year at a nominal annual rate (annual percentage rate) of 6.00%, but you must make interest payments at the end of each month and then pay off the $20,000 principal amount at the end of the year. What is the effective annual rate (EAR) on this loan?

a. 6.00%

b. 6.09%

c. 6.14%

d. 6.17%

e. 6.19%

The correct answer is option (D).

Explanation:

According to the scenario, the given data are as follows:

Payment = $20,000

Annual rate (r) = 6%

Time period (n) = 12 months

So, we can calculate the effective annual rate by using following formula:

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

By putting the value, we get

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

= (((1.005) ^12) - 1)

= (1.06167781186 - 1)

= 0.0617

= 6.17%

Hence, the effective annual rate (EAR) on this loan is 6.17%.