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13 April, 09:43

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%

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Answers (1)
  1. 13 April, 12:08
    0
    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%.
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