Question

Jimmy Hale is the owner and operator of the grain elevator in​ Brownfield, Texas, where he has lived for most of his 62 years. The rains during the spring have been the best in a​ decade, and Mr. Hale is expecting a bumper wheat crop. This has prompted him to rethink his current financing sources. He now believes he will need an additional $ 200 comma 000 for the​ 3-month period ending with the close of the harvest season. After meeting with his​ banker, Mr. Hale is puzzling over what the additional financing will actually cost. The banker quoted him a rate of 2 percent over prime​ (which is currently 6 ​percent) and also requested that the firm increase its current bank balance of ​$4 comma 000 up to 18 percent of the loan. a. If interest and principal are all repaid at the end of the​ 3-month loan​ term, what is the annual percentage rate on the loan offer made by Mr.​ Hale's bank? b. If the bank were to offer to lower the rate to prime if interest is​ discounted, should Mr. Hale accept this​ alternative? Note​: Assume a​ 30-day month and​ 360-day year.

Answer 1

Part (a) Interest = P x r x t = $ 200,000 x (2% + 6%) x 90 / 360 = $  4,000

Compensating balance = 18% of loan = 18% x 200,000 = 36,000

Hence, effective the annual percentage rate on the loan offer = 4,000 / (200,000 - 36,000) x 360 / 90 = 9.76%

Part (b)

Effective the annual percentage rate on the loan offer = 4,000 / (200,000 - 36,000 - 4,000) = 10.00%