You are considering buying a new car for $37,000. If you purchase the car you wi

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?

Explanation / Answer

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

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

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

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