Suppose your firm is seeking a 7-year, amortizing $400,000 loan with annual payments and your bank is offering you the choice between a $410,000 loan with a $10,000 compensating balance and a $400,000 loan without a compensating balance. If the interest rate on the $400,000 loan is 9.5 percent, how low would the interest rate on the loan with the compensating balance have to be in order for you to choose it?
A) The interest rate would have to be lower than 8.76%.
B) The rate would have to be lower than 8.29%.
C) The rate would have to be lower than 8.14%.
D) The rate would have to be lower than 7.99%.

Question

Quizplus · Accepted Answer

The interest rate on the loan with the compensating balance would have to be lower than 8.76% in order for the firm to choose it. This is because the compensating balance effectively increases the interest rate on the loan by reducing the amount of money that the firm can borrow. In this case, the compensating balance is $10,000, which means that the firm can only borrow $390,000. The interest rate on the $400,000 loan is 9.5%, so the effective interest rate on the loan with the compensating balance would be 9.5% * $400,000 / $390,000 = 9.87%. Therefore, the interest rate on the loan with the compensating balance would have to be lower than 8.76% in order for the firm to choose it.

Suppose Your Firm Is Seeking a 7-Year, Amortizing $400,000 Loan