Question

XYZ is deciding among 3 loans that would each involve her receiving $8,000 today and then paying back the original principal and all accrued interest in 1 year from today. Loan A has an APR of 15.50%, compounded annually. Loan B has an APR of 14.80%, compounded quarterly. Loan C has an APR of 14.80%, compounded continuously. Which of the following assertions is true if XYZ prefers loans with lower costs more than she prefers loans with higher costs?

a. XYZ would prefer loan A to loan B and XYZ would prefer loan A to loan C

b. XYZ would prefer loan A to loan B and XYZ would prefer loan

C to loan A c. XYZ would prefer loan B to loan A and XYZ would prefer loan A to loan C

d. XYZ would prefer loan B to loan A and XYZ would prefer loan C to loan A

Answer 1

Effective Annual Rate can be calculated as:

The EAR for Loan A is:

The EAR for Loan B is:

The EAR for Loan C is:

Thus, Loan A has the smallest EAR 15.5%, followed by Loan B 15.64% and then Loan C 15.95%

Therefore, choose Option A.