Question

As a jewelry store manager, you want to offer credit, with interest on outstanding balances paid monthly. To carry receivables, you must borrow funds from your bank at a nominal 4%, monthly compounding. To offset your overhead, you want to charge your customers an EAR (or EFF%) that is 4% more than the bank is charging you. What APR rate should you charge your customers? Round your answer to two decimal places.

Answer 1

First, we need to find the EAR for the borrowed funds;

EAR = [1 + (APR/m)]^m - 1; m = No. of compounding periods in a year

= [1 + (0.04/12)]¹² - 1 = [1.0033]¹² - 1 = 1.0407 - 1 = 0.0407, or 4.07%

EAR charged for customers = EAR for Borrowed Funds + Extra Charge

= 4.07% + 4% = 8.07%

Now, we can find APR charged your customers

EAR = [1 + (APR/m)]^m - 1

0.0807 = [1 + (APR/12)]¹² - 1

[1 + 0.0807]^1/12 = 1 + (APR/12)

1.0065 - 1 = APR / 12

APR = 0.0065 * 12 = 0.0779, or 7.79%