Question

You are considering buying a new car for $37,000. If you purchase the car you will pay $7,000 of the purchase price as a down payment. Below are the two options to choose from.

Option 1: Pay off the amount borrowed to purchase the car with a 5 year loan, and the annual percentage rate (APR) will be 0%.

Option 2: Receive a $2,000 instant rebate. This will lower your loan amount. Pay off the amount borrowed to purchase the car with a 5 year loan, and the annual percentage rate (APR) will be 3.9%

(A) Which option would you choose? Why?

(B) How much should the rebate be in order to make the two options equal?

Answer 1

Purchase price is 37000

down payment is 7000

so remaining balane = 37000-7000 = 30000

option 1; borrow 30,000 & pay in 5 year with 0% APR (so no cost) = 30000/5 = $6000/year

so total payment$30000

otion 2. rebate 2000 so balnce remaining 30000-2000 = 28000

Borrow 28000 in 5 year loan and pay with 3.9% APR

So yarly payment would be 28000/5 = 5600+ Interest as below

Year	Opening balance	Principal	Interest (OB*3.9%)	Total payment	Ending balance
1	28000	5600	1092	6692	22400
2	22400	5600	874	6474	16800
3	16800	5600	655	6255	11200
4	11200	5600	437	6037	5600
5	5600	5600	218	5818
TOTAL		28000	3276	31276

so net payment is $31276.

So we will choose option 1.

2 if rebate is 2000+(31276-30000) = 3276 then both options will be equal