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 14.40%, compounded annually. Loan B has an APR of 13.60%, compounded quarterly. Loan C has an APR of 13.60%, 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

For each of the three loans, we first need to calculate the amount payable after 1 year based on the compounding frequency. The loan with lowest repayable amount will be the picked for the XYZ company.

Loan A

We are given the following information

Amount borrowed	PV	$            8,000.00
rate of interest	r	14.40%
number of years	n	1
Amount Repayable	FV	To be calculated

We need to solve the following equation to arrive at the required FV

So the amount repayable is $9152

Loan B

We are given the following information

Amount borrowed	PV	$            8,000.00
rate of interest	r	13.60%
number of years	n	1
Quartetrly Compounding	frequency	4
Amount Repayable	FV	To be calculated

We need to solve the following equation to arrive at the required FV

So the amount reapyable is $9144.76

Loan C

Amount borrowed	PV	$            8,000.00
rate of interest	r	13.60%
number of years	n	1
Amount Repayable	FV	To be calculated

So amount repayable is 9165.46 rounded off

This means that the loan preferance is Loan B to Loan A to Loan C because Loan B has the lowes repayable amount followed by Loan A and C respectively.

Option c suggests the above mentioned order and is therefore the correct answer.