A firm borrows $100,000 from the bank, but has to maintain a compensating balance of $20,000 with the bank.The annual interest rate for the loan is 12%.What is the effective annual rate if the interest is compounded quarterly?

Question

Quizplus · Accepted Answer

The effective annual rate formula for quarterly compounding with a principal of $80,000 ($100,000 - $20,000 compensating balance) and an interest rate of 12% is:

EAR = (1 + (0.12 / 4))^4 - 1 = 0.1288 or 12.88%

However, since the $20,000 compensating balance is not earning interest, we need to adjust the calculation. The amount of interest paid on the loan is:

Interest = $100,000 x 0.12 = $12,000

The net amount of the loan, after accounting for the compensating balance, is:

Net loan = $100,000 - $20,000 = $80,000

The effective interest rate, adjusted for the compensating balance, is:

EAR = (Interest / (Net loan - Compensating balance)) x (1 / (1 - Compensating balance / Net loan))

EAR = ($12,000 / ($80,000 - $20,000)) x (1 / (1 - $20,000 / $80,000))

EAR = 0.1587 or 15.87%

A Firm Borrows $100,000 from the Bank, but Has to Maintain