Suppose that you're planning a vacation and borrow $2,000 from a bank for one year at a stated annual interest rate of 14 percent, with interest prepaid (a discounted loan).Also, assume that the bank requires you to maintain a compensating balance equal to 20 percent of the initial loan value.What effective annual interest rate are you being charged?

Question

Quizplus · Accepted Answer

The effective annual interest rate can be calculated by considering the actual amount received from the loan and the interest paid. With a 20% compensating balance on a $2,000 loan, you must keep $400 (20% of $2,000) in the bank, effectively receiving only $1,600 ($2,000 - $400). However, you still pay interest on the full $2,000 at 14%, which is $280. The effective interest rate is then $280 interest paid divided by the $1,600 actually received, which equals 17.5%. However, because the interest is prepaid, the calculation should adjust for this, leading to an effective rate higher than initially calculated, specifically 21.21%.

Suppose That You're Planning a Vacation and Borrow $2,000 from a Bank