You have just taken out a loan for $75,000. The stated (simple) interest rate on this loan is 10 percent, and the bank requires you to maintain a compensating balance equal to 15 percent of the initial face amount of the loan. You currently have $20,000 in your checking account, and you plan to maintain this balance. The loan is an add-on installment loan which you will repay in 12 equal monthly installments, beginning at the end of the first month.
-Wentworth Greenery harvests its crops four times annually and receives payment for its crop 90 days after it is picked and shipped. However, the firm must plant, irrigate, and harvest on a near continual schedule. The firm uses 90-day bank notes to finance its operations. The firm arranges an 11 percent discount interest loan with a 20 percent compensating balance four times annually. What is the effective annual interest rate of these discount loans?

Question

Quizplus · Accepted Answer

The effective annual interest rate (EAR) for a discount loan with a compensating balance can be calculated using the formula: EAR = (Interest / (Loan Amount - Compensating Balance)) * (365 / Loan Term). For Wentworth Greenery, the interest is 11% of the loan amount, and the compensating balance is 20% of the loan amount. The loan term is 90 days. Calculating this gives an EAR of approximately 15.94%.

You Have Just Taken Out a Loan for $75,000