Your bank offers you a line of credit of $35,000 with an interest rate of 1.95 percent per quarter. The loan agreement also requires that 2 percent of the unused portion of the credit line be deposited in a non-interest-bearing account as a compensating balance. Your short-term investments are paying .17 percent per month. What is your effective annual interest rate on this arrangement if you do not borrow any money during the year? Assume any funds borrowed or invested use compound interest.

Question

Quizplus · Accepted Answer

The effective annual interest rate when no money is borrowed is essentially the opportunity cost of the compensating balance requirement. Since 2% of the $35,000 credit line must be kept in a non-interest-bearing account, this is $700 that could have been earning interest elsewhere. Given the short-term investments pay 0.17% per month, the annualized rate (using compound interest) is (1 + 0.0017)^12 - 1 = 0.0206 or 2.06%. This calculation reflects the lost opportunity to earn interest on the $700, not an interest expense directly charged by the bank.

Your Bank Offers You a Line of Credit of $35,000