Question

You are considering buying a sports car with a list price of $99,000. The dealer has offered you two payment alternatives: - You can get a $9,000 discount if you pay cash today. - You can buy the car for the list price of $99,000. You need to make a down payment of $39,000. The remainder $60,000 is a "zero-interest loan" to be paid back in equal installment over 36 months. Alternatively, your bank is willing to give you a car loan with APR of 10%, compounded monthly. Decide how to finance the car: bank loan, zero-interest loan with the dealer, or cash payment.

Answer 1

Please see below the results I have pasted from my excel sheet:

We have three options:

Under option 1, the effective price of the car is 99,000-9,000 = $90,000 which is paid down today

Under option 2, the effective price of the car is a downpayment of 36,000 + present value of all 36 EMIs which turns out to be a total of $55,128

Under option 3, through the loan, the present value (effective price) of the car will be same $99,000

Hence, option 2 - downpayment + zero-interest loan is preferred

Formula used in excel: Present value at 10% for EMI = PV(10%,36,60,000/36,0)*-1; For

List price of car	99,000
Option 1
9,000 cash discount
Effective price of car	90,000
Option 2
Downpayment	39,000
zero-interest loan	60,000
Months to pay back	36
EMI	1,666.67
Present value @ 10%	16,128
Effective price of car	55,128
Option 3
Car loan	99,000
APR	10%
Compounded	monthly
Effective price of car	$ 99,000