Question

Montross Inc. needs to raise $200,000 for a nine-month term. Montross’s bank has offered to lend Montross the money at a 16.00% simple interest rate. Montross will receive the $200,000 upon approval of the loan and will pay back the principal and interest at maturity.

Calculate the interest payment, the amount of cash received, the annual percentage rate (APR), and the effective annual rate (EAR) of this loan.

	Value
Interest payment	1. A. 21120 B. 32000 C 28160 D. 24000
Amount of cash received	2. A. 200,000 B. 224000 C. 176000 D 171840
Annual percentage rate (APR)	3. A. 16.00 % B. 9 C. 12 D 13
Effective annual rate (EAR)	4. A 16.00% B. 8.87 C 16.31 D 12

Suppose the terms of the loan require that Montross maintain a compensating balance equal to 5% of the loan balance, and Montross will have to borrow the compensating balance from the bank.

Calculate the interest payment, the amount of cash received, the annual percentage rate (APR), and the effective annual rate (EAR) of the loan considering the compensating balance requirement.

Interest payment	5. A. 20,210 B. 30316 C. 25263 D 40421
Amount of cash borrowed	6. A. 168,421 B 252631 C 210,526 D 336842
Annual percentage rate (APR)	7.A. 0.77% B 1.57% C. 16.84 D 2.37
Effective annual rate (EAR)	8.A 19.39% B 18.59 C 17.19 D 17.79

Answer 1

1.

Value
Interest payment	$200000 * 16% * 9 / 12 = $24000 D
Amount of cash received	Given $200000 A
Annual percentage rate (APR)	A 16% as it is a simple interest
Effective annual rate (EAR)	(1 + 0.12)^12/9 - 1 = 16.31% C

2.Loan Amount = Requirement / (1 - Compensating) = $200000 / 0.95 = $210526.31

Interest payment	$210526.31 * 16%*9/12 = $25263 C
Amount of cash borrowed	Loan Amount = $210526 B
Annual percentage rate (APR)	25263 / 200000 * 12/9 = 16.84% C
Effective annual rate (EAR)	(1 + 16.84%*9/12)^(12/9) - 1 = 17.19% C