Imagine that you have decided you need a new car, but not any car will do; you have decided to purchase the car of your dreams. 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 questions:
· What type of car have you selected, and what will it cost?
· What is the 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 provided in Chapter 4 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 provided in Chapter 4 and show your work. How much will that car have cost in 3 years?
· Which is the better deal and why?
What type of car have you selected, and what will it cost? The car I have selected is a 2009 BMW545i for $26,280. What is the interest rate from your local bank for a car loan for four years? The interest rate for four years at my bank USAA is 1.99%. What will your payments be to your local bank, assuming your 10% down payment and how much will that car have cost in four years? The payments at my local bank will be below looking at the equations with the 10% down.
PVₒ = $23,652 (after 10%) r = .0199 (1.99%) n = 48 (4 year loan)
PVo = PMT ( 1 – [1/ (1 + r) N] ) r $23,652 = (PMT) ( 1 – [1/ (1 + .0199)48] ) .0199 $23,652 = (PMT) ( 1 – [1/ (1.0199)48] ) .0199 $23,652 = (PMT) ( 1 – [1/ 2.574923943483174] ) .0199 $23,652 = (PMT) ( 1 – 0.3883609853917748 ) .0199 $23,652 = (PMT) ( 0.6116390146082252 ) .0199 $23,652 = (PMT) [30.7356] PMT = $23,652 / 30.7356 The PMT= $769.53 So after four years, this car would have cost a total of $36,937.44 with $769.53 payments every month. So the total interest over the four year timeframe will be $13,285.44. What will be your payment to the dealership finance company assuming your 10% down payment and how much will that car have cost in three years? By using the amortization formula the PVₒ = $23,652 (after 10%) r = .1000 (10%) = 36 (3 year loan) PVo = PMT ( 1 [1/ (1 + r)N] ) r $23,652 = (PMT) ( 1 – [1/ (1 + .1000)36] ) .1000 $23,652 = (PMT) ( 1 – [1/ (1.1000)36] ) .1000 $23,652 = (PMT) ( 1 – [1/ 30.91268053287067] ) .1000 $23,652 = (PMT) ( 1 – .0323491843076067 ) .1000 $23,652 = (PMT) ( .967650815692393 ) .1000 $23,652 = (PMT) [9.6765815692393] PMT = $23,652 / 9.6765 PMT = $2444.27 each month
After three years, this car would have cost a total of $87,993.72 ($2444.27*36). Total interest would have been $64,341.72 which all together is a lot. The 5% rebate ($1,181.25) at the end of the three year term would not even matter because I would have so much interest still left that it would take me along time just working my way to the principle. Which by then the car would not be worth anything and I would be upside down. Which is the better deal and why? The better deal is the bank loan as you can see by my calculations. I would rather pay $13,000 in interest which is still a lot versus all together over $64,000. So with that being said since the bank loan offers 1.99% it is still better than the 10% the dealership is offering because of the longer terms will make your payment every month be affordable. I will say that if I had more than 10%percent to put down that will be a plus because every $1000 you put down knocks off $25 from your car payment. So the more you put down the lower your payments will be every month which in the end makes sense.
Reference:
Hickman, K. A., Byrd, J. W., & McPherson, M. (2013). Essentials of finance. San Diego, CA: Bridgepoint Education Inc.
