Question

(10 points) You ran a little short on your vacation. You have two options: • Option 1: Put $1,000 on your credit card. The annual interest rate on the credit card is 12% compounded monthly. Option 2: Take out a $1,000 short-term loan from CIBC with annual percentage rate of 12.4% compounded quarterly. a) Which option would you choose? Why? b) Let's say you conclude that you better off using your credit card (Option 1). You can only afford to make the payment of $20 per month. How long will you need to pay off the $1,000?

Answer 1

a]

I would choose the option with the lower effective annual rate (EAR)

EAR = (1 + (r/n))ⁿ - 1

where r = annual rate

n = number of compounding periods per year.

n = 12 for the credit card as it is compounded monthly.

n = 4 for the loan as it is compounded quarterly.

EAR of credit card = (1 + (12%/12))¹² - 1 = 12.68%

EAR of loan = (1 + (12.4%/4))⁴ - 1 = 12.99%

I would choose the credit card as the EAR is lower

b]

Number of months to pay off is calculated using NPER function in Excel :

rate = 12%/12 (monthly rate = annual rate / 12)

pmt = -20 (Monthly payment. This is entered with a negative sign because it is a payment)

pv = 1000 (amount borrowed on credit card)

NPER is calculated to be 69.66.

It will take 69.66 months to pay off the credit card

A1 x fc =NPER(12%/12,-20,1000) D E F B C A 69.66 1