Question

2. A financial company is going to borrow $5 million for 3 months. The company has three options: A. a commercial bank offering a 5% annual rate loan; B. an insurance firm can provide a 4.4% annual rate discount loan and C. a brokerage can provide a 4% annual rate loan with 8% compensation balance. a) What is the effective annual rate for each option assume that the company has no any deposit in each organization? b) Which option should the company use to borrow money?

Answer 1

a). Effective Annual Rate (EAR) for 5% annual rate loan = 5%

EAR for 4.4% annual discount loan: Interest = 4.4%*5 = 0.22 million

EAR = interest/(principal-interest) = 0.22/(5-0.22) = 4.60%

EAR for 4% annual rate loan with 8% compensating balance:

Interest = 4%*5 = 0.20 million

Compensating balance = 8%*5 = 0.40 million

Net principal = 5-0.40 = 4.60 million

EAR = 0.20/4.60 = 4.35%

b). The cheapest loan is the compensating balance loan so that should be taken.