True or false: If the annual interest rate is 18%, the monthly interest rate is 1.5%.

True or false: If the annual interest rate is 18%, the monthly interest rate is 1.5%.

• A. True
• B. Not enough information
• C. Both
• D. False

Answer: (D)

The key idea is that converting an annual rate to a monthly rate depends on whether the annual rate is a nominal rate with monthly compounding or an effective annual rate. If the 18% is a nominal rate with monthly compounding, the monthly rate is simply 18% divided by 12, which is 1.5% per month. But if 18% is the effective annual rate, the monthly rate cannot be 1.5%; it must satisfy (1 + i)^12 = 1.18, so i = (1.18)^(1/12) − 1 ≈ 1.389% per month. Since the problem doesn’t specify which interpretation is intended, you cannot state that the monthly rate is 1.5% in all cases. Therefore the statement is not universally true.

The key idea is that converting an annual rate to a monthly rate depends on whether the annual rate is a nominal rate with monthly compounding or an effective annual rate. If the 18% is a nominal rate with monthly compounding, the monthly rate is simply 18% divided by 12, which is 1.5% per month. But if 18% is the effective annual rate, the monthly rate cannot be 1.5%; it must satisfy (1 + i)^12 = 1.18, so i = (1.18)^(1/12) − 1 ≈ 1.389% per month. Since the problem doesn’t specify which interpretation is intended, you cannot state that the monthly rate is 1.5% in all cases. Therefore the statement is not universally true.