Finance: TVM Concept / Simple Interest Amortized Auto Loan

Imagine that you have decided you need to a purchase 2015 Range Rover Land Rover for $83,500. Conduct some research as to the cost of this car.  You have determined in this imagined scenario that you could afford to make a 10% down payment.  You can borrow the balance either from your local bank using a four-year loan or from the dealership’s finance company.  If you purchase from your dealership’s finance company, the APR will be 10% with your 10% down and monthly payments over three years. However, the dealership will give you a rebate of 5% of the car price after the three year term is complete.  You want the best deal possible, so you consider the following:

An amortized loan is a direct application of the present value of an annuity. The original amount borrowed is the present value of the annuity (PV0), while loan payments are the annuity’s cash flows (CFs)

2015 Range Rover Land Rover for $83,500

2.5% interest rate from your local bank for a car loan for four years

• What will your payment be to your local bank, assuming your 10% down payment? Be sure to use the formula for a simple interest amortized auto loan and show your work. How much will that car have cost in four years?
• What will your payment be to the dealership finance company assuming your 10% down payment? Be sure to use the formula for a simple interest amortized loan and show your work. How much will that car have cost in 3 years?
• Which is the better deal and why?