You are considering two loans. The terms of the two loans are equivalent with the exception of the interest rates. Loan A offers a rate of 7.75 percent, compounded daily. Loan B offers a rate of 8 percent, compounded semi-annually. Which loan should you select and why?

Question

Quizplus · Accepted Answer

We need to calculate the effective annual rates of both loans to compare them.

Loan A: 
Daily rate = 7.75%/365 = 0.0212%
Effective annual rate = (1 + 0.000212)^365 - 1 = 8.06%

Loan B: 
Semi-annual rate = 8%/2 = 4%
Effective annual rate = (1 + 0.04)^2 - 1 = 8.16%

Therefore, Loan A has a lower nominal rate but a higher effective annual rate, making it the better choice.

You Are Considering Two Loans