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

To compare the two loans, we need to calculate the effective annual rate (EAR) for both. Loan A has a daily compounding frequency, so we use the following formula:

EAR = (1 + r/n)^n - 1
where r is the annual interest rate and n is the compounding frequency per year. Plugging in the values for Loan A, we get:

EAR = (1 + 0.0775/365)^365 - 1
EAR = 0.0806 or 8.06%

For Loan B, we use the same formula but with a semi-annual compounding frequency:

EAR = (1 + r/n)^n - 1
EAR = (1 + 0.08/2)^2 - 1
EAR = 0.0816 or 8.16%

Since Loan A has a lower interest rate but a higher compounding frequency, it results in a slightly higher effective annual rate. Therefore, the better choice is Loan A.

You Are Considering Two Loans