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? a. the annual percentage rate is 7.68 percent. b. the annual percentage rate is 7.15 percent. c the effective annual rate is 8.16 percent. d. the effective annual rate is 8.06 percent.

Question

Jazmine Knox

Business

11 December, 18:37

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? a. the annual percentage rate is 7.68 percent. b. the annual percentage rate is 7.15 percent. c the effective annual rate is 8.16 percent. d. the effective annual rate is 8.06 percent.

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Answers (1)

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Tiana Cooke · Answer 1

You should go for Loan B because its Effective Interest Rate is better than that of Loan A.

c. The effective annual rate is 8.16 percent.

Explanation:

We cannot make decisions based on the Nominal Interest Rates. So, we have to look at the Effective interest rates of each investment option because Effective Interest Rate takes the effect of compounding into account. The formula of Effective Interest Rate is:

r = [ (1 + i / n) ^ n] - 1

where

r = Effective Interest Rate

i = Nominal Interest Rate that is the interest rate states

n = No. of compounding periods.

Effective Interest Rate of Loan A = 8.057%.

Effective Interest Rate of Loan B = 8.16%.

So, it can seen that Loan B generates a better return.