Suppose a bank offers to lend you $10,000 for 1 year on a loan contract that calls for you to make interest payments of $200.00 at the end of each quarter and then pay off the 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 by considering the quarterly interest payments and the principal repayment at the end of the year. The quarterly interest payment is $200, and there are four payments per year, totaling $800 in interest for the year on a $10,000 loan. However, to find the EAR, we must account for the compounding effect of the quarterly payments. The formula to calculate the EAR in this scenario, given the quarterly compounding, is: $$EAR = \left(1 + \frac{i}{n}\right)^n - 1$$ where $i$ is the annual interest rate and $n$ is the number of compounding periods per year. Since the question does not directly provide the annual interest rate but gives quarterly payments, we approach it by recognizing that the EAR reflects the equivalent annual interest rate considering compounding. The correct EAR, given the options, is 8.24%, which accounts for the compounding effect of making quarterly interest payments on the loan. This choice is derived from calculating the effective interest rate considering the structure of the payments, not from the simple interest calculation.

Suppose a Bank Offers to Lend You $10,000 for 1