Suppose United Bank offers to lend you $10,000 for one year at a nominal annual rate of 8.00%, but you must make interest payments at the end of each quarter and then pay off the $10,000 principal amount at the end of the year.What is the effective annual rate on the loan?

Question

Quizplus · Accepted Answer

The effective annual rate (EAR) can be calculated using the formula for compound interest when interest is compounded quarterly. The nominal annual rate is 8.00%, and since interest is paid quarterly, the quarterly interest rate is 8.00% / 4 = 2.00%. The formula for EAR when interest is compounded quarterly is (1 + (nominal rate / number of compounding periods))^number of compounding periods - 1. Plugging in the values, we get (1 + 0.08/4)^(4) - 1 = (1 + 0.02)^(4) - 1 = 1.08243216 - 1 = 0.0824 or 8.24%.

Suppose United Bank Offers to Lend You $10,000 for One