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Cost of Bank Loans Del Hawley, owner of Hawley’s Hardware, is negotiating with First City Bank for a 1-year loan of $90,000. First City has offered Hawley the alternatives listed below. Calculate the effective annual interest rate for each alternative. Do not round intermediate calculations. Round your answers to two decimal places. A 12% annual rate on a simple interest loan, with no compensating balance required and interest due at the end of the year. 12 % A 8% annual rate on a simple interest loan, with a 20% compensating balance required and interest due at the end of the year. 10 % A 8.75% annual rate on a discounted loan, with a 15% compensating balance. 11.28 % Interest figured as 9% of the $90,000 amount, payable at the end of the year, but with the loan amount repayable in monthly installments during the year. 15.62 % Which alternative has the lowest effective annual interest rate? Alternative B

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Answer:

Calculate the effective annual interest rate for each alternative.

A 12% annual rate on a simple interest loan, with no compensating balance required and interest due at the end of the year.

  • you borrow $90,000 and pay $10,800 in interests, effective rate = 12%

A 8% annual rate on a simple interest loan, with a 20% compensating balance required and interest due at the end of the year.

  • you borrow $90,000, but you only take home $72,000. You pay $7,200 in interests, therefore, effective interest rate = $7,200 / $72,000 = 10%

A 8.75% annual rate on a discounted loan, with a 15% compensating balance. 11.28 %

  • you borrow $90,000, but you only take home $90,000 - $7,875 (discounted interest) - $13,500 (15% compensating balance) = $68,625. You pay back $76,500, so interest = $7,875. Effective interest rate = $7,875 / $68,625 = 11.48%

Interest figured as 9% of the $90,000 amount, payable at the end of the year, but with the loan amount repayable in monthly installments during the year.

  • you take home $90,000, but the first 11 months you pay $7,500 and the last payment = $15,600. Using a financial calculator, I just calculated the monthly IRR = 1.2621%. The effective interest rate = (1 + 1.2621%)¹² - 1 = 16.24%

Which alternative has the lowest effective annual interest rate?

Alternative B:

A 8% annual rate on a simple interest loan, with a 20% compensating balance required and interest due at the end of the year.