Section B 20(a) Your company has a line of credit through a local bank. The bank

Question

Section B 20(a) Your company has a line of credit through a local bank. The bank requires a 690 compensating balance and charges 12% on the amount borrowed against the line. If the company needs $100,000 to purchase inventory, find the amount it should borrow, and calculate the effective annual rate on the loan. You've worked out a line of credit arrangement that allows you to borrow up to $100 million at any time. The interest rate is 0.4 percent per month. In addition, 5% of the amount that you borrow must be deposited in a non-interest bearing account (i.e. a compensating balance). Assume that your bank uses compound interest on its line of credit loans. What is the effective annual rate (EAR) on the loan? What is the APR on the loan? Which rate would the bank advertise -the APR or the EAR? (b)

Explanation / Answer

20.(a) The company has to borrow an amount which after providing for the compensating balance will equal the amount required for the purchase--$100,000 So, 100000 = 100%-6% = 94% Loan amount = 100000/94% = $            106,382.98 Interest on the loan amount = 106382.98*12% = $              12,765.96 Effective annual rate = 12765.96/100000 = 12.77% Answer 20.(b) Amount received net of compensating balance = 100000000*95% = $      95,000,000.00 Total interest charged for a year = 100000000*(1.004^12-1) = $        4,907,020.75 Effective annual rate of interest = 4907020.75/95000000 = 5.17% Monthly rate: 0.0517 = (1+r)^12-1, where r is the monthly rate. Solving for r r = 1.0517^(1/12)-1 = 0.0042 APR = 0.0042*12 = 5.04% Answer

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