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
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.
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