Applied Math - Finances - Buying a Car

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Introduction

There are many calculations that go into buying a car. Some states have different taxes for purchasing a car. Dealerships will sometimes add on a cost at the time of signing papers that is unique to that dealership.

If your vehicle is used for a business, you can reduce your taxable income by calculating the depreciation of the vehicle. There are several methods for doing this. The simplest method is the straight-line method.

Below are some of the calculations that should be made when considering the purchase of a car.

Example:

1.
https://www.youtube.com/watch?v=s01vT0bVSUk
A person has decided that they should be able to negotiate 5% off the manufacturer’s suggested retail price (MSRP) of a car. If a car is selling for \(\$34,500\), how much should the person try to pay for the car?

To calculate 5% less than a quantity, we could calculate 5% of that quantity then subtract it from the quantity. A quicker way is to calculate 95% of the price. If we get 5% off, then we pay \(100\% - 5\% = 95\%\) of the original price.

\[\$34,500 \cdot 0.95 = \$32,775\]



2.
https://youtu.be/s01vT0bVSUk?si=fj2nfk5MkDiwjh-C&t=72
The agreed purchase price of the above vehicle is \(\$33,000\). The state tax is 5.5%. Title and registration fees are $150. There is a documentation and processing fee of $500. The person purchasing the car is taking out a loan through the dealership. There is a loan origination fee of 1% of the purchase price. What is the total amount of money owed when purchasing this vehicle, including the purchase price?

The tax is \(\$33,000 \cdot 0.055 = \$1,815\)

The origination fee is \(\$33,000 \cdot 0.01 = \$330\).

Adding these to the purchase price, the total money owed is

\[\$33,000 + \$1,815 + \$330 + \$150 + \$500 = \$35,795\]



3.
https://youtu.be/s01vT0bVSUk?si=XWDnCrrPFRvy3n11&t=125
You could save up money for a down payment or you could finance the entire price of the car.

If you have no down payment and you take out a 5 year loan at 6% interest, the monthly payments for the above car would be $692.02.

If you have a $10,000 down payment and you take out a 5 year loan at 6% interest, the monthly payments for the above car would be $498.69.

How much would the $10,000 down payment save in the length of the loan, assuming only the monthly payments are made (no extra payments)?

If the loan is for 5 years, there are 60 payments of $692.02 under the first option and $498.69 under the second option.

\[\text{first option } = \$692.02 \cdot 60 = \$41,521.20\]

\[\text{second option } = \$498.69 \cdot 60 + \$10,000 \]

\[\ \text{ down payment} = \$39,921.40\]

Using a $10,000 down payment means we have saved

\(\$41,521.20 - \$39,921.40 = \$1,599.80\)

Practice Problems

1. A person has decided that they should be able to negotiate 6% off the manufacturer’s suggested retail price (MSRP) of a car. If a car is selling for \(\$29,495\), how much should the person try to pay for the car?



2. The agreed purchase price of the above vehicle is \(\$27,500\). The state tax is 5.5%. Title and registration fees are $250. There is a documentation and processing fee of $400. The person purchasing the car is taking out a loan through the dealership. There is a loan origination fee of 1% of the purchase price. What is the total amount of money owed when purchasing this vehicle, including the purchase price?



3. Suppose you are financing \(\$29,000\) for a car. You could finance the entire cost, or you could make a $5,000 down payment. If you finance the entire car, your monthly payment for 60 months is $586.23. If you make a down payment of $5,000, your monthly payment for 60 months is $532.42. How much money has been saved over the course of the loan (assuming no extra payments are made) by making the $5,000 down payment?

Theory Questions

1. What strategies could be used in negotiating the fair purchase price of a car? Are there resources to determine a fair price outside the car dealership?