You are considering buying a sports car with a list price of $99,000. The dealer

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.

Explanation / Answer

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

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