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

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