Robertson Lumber has a $250,000 compensating balance loan with its bank. The terms of the loan call for Robertson to keep 10% of the loan as a compensating balance and pay interest at an annual rate of 6.50% on the entire amount. If the firm borrows the maximum amount for one year, what is the EAR on this loan?

Question

Quizplus · Accepted Answer

First, we need to calculate the amount of the loan after the compensating balance is taken into account.

Compensating balance = 10% of loan = 0.10 x $250,000 = $25,000

Loan amount = $250,000 - $25,000 = $225,000

Next, we need to calculate the effective interest rate on the loan.

EAR = (1 + APR/n)^n - 1

Where APR is the annual percentage rate (6.50%), and n is the number of compounding periods in one year.

Since the loan is for one year and interest is compounded annually, n = 1.

EAR = (1 + 0.065/1)^1 - 1 = 0.065 or 6.50%

However, this calculation does not take into account the compensating balance requirement. To adjust for the compensating balance, we can use the following formula:

Adjusted EAR = (1 + APR/n)/(1 - B) - 1

Where B is the percentage of the loan that must be held as a compensating balance (10%).

Adjusted EAR = (1 + 0.065/1)/(1 - 0.10) - 1 = 0.0722 or 7.22%

Therefore, the best choice is C, 7.22%.

Robertson Lumber Has a $250,000 Compensating Balance Loan with Its