Question

​(Cost of a​ short-term bank loan​) 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 $220,000 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 8 percent) and also requested that the firm increase its current bank balance of $4,000 up to 22 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

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?
	Net funds needed	220,000.00
	Funds needed to be maintained in bank balance	48,400.00
	Total Loan amount needed	268,400.00
	Rate of interest p.a. (8%+2%)	10%
	Rate of interest for the quarter	2.50%
	Amount of interest paid	6,710.00
	Effective interest on funds needed	3.05%	6710/220,000*100
b	If the bank were to offer to lower the rate to prime if interest is​ discounted, should Mr. Hale accept this​ alternative?
	Net funds needed	220,000.00
	Rate of interest p.a. (8%)	8%
	Rate of interest for the quarter	2.00%
	Total Loan amount needed assuming interest is discounted upfront	224,489.80	220,000/(100%-2%)
	Amount of interest	4,489.80	224489.79*2%
	Effective interest on funds needed	2.04%
	Since effective interest rate is lower here, hence offer should be accepted