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 semi-annually?

Question

Quizplus · Accepted Answer

The effective annual rate (EAR) is calculated by considering the actual amount available for use, which is $80,000 ($100,000 - $20,000). The nominal interest rate is 12%, compounded semi-annually, so the semi-annual rate is 6%. The formula for EAR is (1 + r/n)^(n*t) - 1, where r is the nominal rate, n is the number of compounding periods per year, and t is the time in years. Adjusting for the compensating balance, the effective rate becomes higher, resulting in 15.56%.

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