Question

A store offers you a 5% discount on the cost of your purchase if you pay cash today.

Otherwise, you will be billed the full price with payment due in a quarter.

The third option is you will be billed 33% of the cost for the following three months.

1) What is the implicit borrowing rate (effective annual interest rate) being paid by customers who choose to defer payment for a quarter?

2) What is the implicit borrowing rate (effective annual interest rate) being paid by customers who choose the installment?

3) Now suppose you have to defer the payment, and the offered EAR of your credit card company is 27%, which purchase option would you prefer?

Answer 1

As given in the question, the the cost of the purghase is $95.

1. Cash = $95

2. Payment after a quarter = $100

3. 3 monthly installments = $33 each

1. The effective annual rate for option 2 is:

CAGR = (100/95)4 - 1 = 22.77%.

2. EAR for option 2 is:

PV = Installment value * (1-(1+R)-n​​​​​)/R

where, Installment Value is $33, PV is $95 and n is 3

Putting values, we get R (monthly interest) = 2.09% PM = 25% PA

3. If the EAR of credit card is 27%, we'll choose option 3 as once $33 is paid, next month's interest will be applicable on $66 and so on.