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 monthly?

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The effective annual rate (EAR) can be calculated considering the actual amount available for use from the loan after maintaining the compensating balance. The firm borrows $100,000 but must keep $20,000 in the bank, leaving $80,000 for use. The interest rate is 12% annually, but with monthly compounding, we need to find the effective annual rate on the actual amount used ($80,000). The nominal interest paid is $12,000 ($100,000 * 12%), but since only $80,000 is effectively used, the effective interest rate is $12,000/$80,000 = 15%. However, with monthly compounding, the EAR is higher than the nominal rate. The formula for EAR with monthly compounding is (1 + r/n)^(n*t) - 1, where r is the annual nominal rate, n is the compounding frequency per year, and t is the time in years. Substituting r = 0.15 (since we're considering the effective rate of interest on the usable funds), n = 12, and t = 1, we get an EAR higher than 15%, which aligns closest with option D, 16.08%. The exact calculation for EAR considering the compensating balance and the effective use of funds leads to recognizing the higher cost of borrowing, which is effectively captured by option D.

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