Come and Go Bank offers your firm a discount interest loan with an interest rate
ID: 2795665 • Letter: C
Question
Come and Go Bank offers your firm a discount interest loan with an interest rate of 7 percent for up to $20 million, and in addition requires you to maintain a 4 percent compensating balance against the face amount borrowed.
What is the effective annual interest rate on this lending arrangement? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)
Come and Go Bank offers your firm a discount interest loan with an interest rate of 7 percent for up to $20 million, and in addition requires you to maintain a 4 percent compensating balance against the face amount borrowed.
Explanation / Answer
You will pay interest of:
Interest = $20,000,000 * (0.07)
Interest = $1,400,000
Additionally, the compensating balance on the loan is:
Compensating balance = $20,000,000 * (0.04) = $800,000
Since this is a discount loan, you will receive the loan amount minus the interest payment. You will also not get to use the compensating balance. So, the amount of money you will actually receive on a $21 million loan is:
Cash received = $20,000,000 - 1,400,000 - 800,000 = $17,800,000
The EAR is the interest amount divided by the loan amount, so:
EAR = $1,400,000/ 17,800,000
EAR = 7.87%