The Boyles Ceramics,Inc.established a line of credit with a local bank.The maximum amount that can be borrowed under the terms of the agreement is $1,000,000 at an annual rate of 8 percent.A compensating balance averaging 25 percent of the amount borrowed is required.Prior to the agreement,Boyles had no deposit with the bank.Shortly after signing the agreement,Boyles needed $240,000 to pay off a note that was due.Boyles decides to borrow an amount sufficient to pay the $240,000 note and also to cover the compensating balance.What is the effective annual cost of credit if the loan is made on a discount basis?
A) 11.94%
B) 11.00%
C) 10.83%
D) 10.57%

Question

Quizplus · Accepted Answer

The effective annual cost of credit is calculated by considering the amount borrowed, the interest charged, and the compensating balance requirement. Since the loan is on a discount basis, the interest is deducted upfront. To find the amount Boyles needs to borrow to have $240,000 after accounting for the compensating balance, we use the formula: Amount Needed = Desired Amount / (1 - Compensating Balance Percentage). Here, it's $240,000 / (1 - 0.25) = $320,000. The interest on this amount at 8% is $25,600. However, since the loan is on a discount basis, Boyles effectively receives $320,000 - $25,600 = $294,400 but needs to ensure $240,000 after the compensating balance. The effective annual cost is then calculated based on the net amount received versus the actual amount used ($240,000), leading to an effective rate higher than the nominal 8%, specifically 11.94%.