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 6%, monthly compounding. To offset your overhead, you want to charge your customers an EIR that is 2% more than the bank is charging you. What annual interest rate should you change your customers?

Answer 1

To offset borrowing costs from a bank and additional overhead, the jewelry store manager should charge an annual interest rate of 8.17%, which is 2% higher than the bank's effective annual rate of 6.17%.

Step-by-step explanation:

The question requires calculating an annual interest rate that a jewelry store manager should charge customers to offset borrowing costs from a bank and additional overhead. The bank's nominal rate is 6% with monthly compounding, and the store manager wants to charge 2% more as the Effective Interest Rate (EIR).

To begin with, we need to convert the bank's nominal rate to the EIR. Given that the bank's rate is compounded monthly, we would use the formula EIR = (1 + nominal rate / compounding periods) ^ compounding periods - 1. Substituting the given values, EIR = (1 + 0.06/12) ^ 12 - 1, which gives us approximately 0.0617 or 6.17% annually.

To find the rate to charge customers, we add 2% to the bank's EIR, which gives us 6.17% + 2% = 8.17%. Therefore, the annual interest rate to charge customers would be 8.17%.