Question

3. (30 points) Last Bank of Podunk is lending a business $150,000. The loan has a 6% stated interest rate and matures in 1-year. In each case below tell 1) how much you borrow and 2) compute the actual interest rate on the loan (show answer in percent with two decimal places). a) The loan requires a 25% compensating balance. b) The loan is a discount loan where the interest is taken from the proceeds at the beginning of the loan. c) The loan is structured as an installment loan with add-on interest requiring 12 monthly payments.

Answer 1

a). Borrowing amount = loan*(1-compensating balance) = 150,000*(1-25%) = 112,500

Actual interest rate = interest rate/(1-compensating balance) = 6%/(1-25%) = 8.00%

b). Interest on loan = 6%*150,000 = 9,000

Borrowing amount = principal - interest = 150,000 - 9,000 = 141,000

Actual interest rate = interest/borrowing amount = 9,000/141,000 = 6.38%

c). Borrowing amount = 150,000

Total amount = principal + interest = 150,000 + 9,000 = 159,000

Monthly payment = total amount/12 = 159,000/12 = 13,250

PV = 150,000; PMT = -13,250; N = 12, solve for RATE.

Monthly rate = .91% so annual rate = 0.908%*12 = 10.90%