The selling price of your new car is $33,000. At the time of purchase, you are o
ID: 3120250 • Letter: T
Question
The selling price of your new car is $33,000. At the time of purchase, you are offered the following two options:
Option 1: 0% financing for 60 months
Option 2: $7,000 instant rebate off the price of the car. Finance the remaining balance with a bank loan, described below.
For option 2, the bank is willing to offer you a loan with an annual interest rate of 5.2%, with interest compounded monthly. The loan has a term of 4 years.
(a) Under option 1, if you make the same payment at the end of each month with the intention of paying off your loan at the end of the 60 months, what is your monthly payment? What is the total that you would pay for the car with this option?
(b) Under option 2, if you make the same payment at the end of each month with the intention of paying off your loan at the end of the 4 years, what is your monthly payment? What is the total that you would pay for the car with this option?
Explanation / Answer
Lets analyze opiton one by one
Option 1:
0% financing for 60 months.
Price of the car is 33000
Monthly payment = 33000/60 = $550
Hence under opiton 1, monthly payment would be $550 and the total amount paid for the car is $33000.
Option 2:
If one take a loan from the bank, $7000 is waived off on the selling price. Hence the new price would be 33000 - 7000 = $26000.
Interest rate per month = (5.2/100)/12 = 0.0043
period n = 48 months
Total amount to be paid after compounding = 26000 * (1+0.0043)^48 = 31997.16
Monthly payment = 31997.16/48 = $666.61
Total amount paid under this option is $31997.16
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