**Wheeling Deals**

**Sonya Gonzalez Maureen Newman Kim Reinholt**

Class: Algebra II

**Materials:** Graph paper

**Goals: **Use linear graphs to interpret data, research and interpret expenses to fit income

constraints, and make decisions as a group

**Time Required:** Out of class project taking a period of two to three weeks

**Background:** Reading, using, and organizing data, developing linear equations, graphing linear equations, solving systems of equations, communication, and group activity skills

**Setting: **This project is intended to have students research and analyze all expenses of purchasing and owning a car. Analysis will be accomplished through use of linear equations and their graphs.

**Problem:** (See also attached student sheet)

You are going to purchase your first car. Your financial resources include a bank account of $1500 and a part-time job where you earn $100 per week. You are to research at least three different cars, one of which must be new and one that must be used. The data you gather must include **ALL** the expenses of owning and maintaining a car for the first year.

Among the items that are expected to be in your written and oral reports are: 1) a list of assumptions; 2) documentation or justification of all the data gathered; 3) cost-mileage equations for each car and the corresponding graph (with intersections for at least two pair of equations); and 4) a statement of analysis including the car of choice (clearly justified) and statement of what information can be gained from the graph.

**Solution:**

We begin with our list of assumptions.

1. The figures used are for the first year of ownership.

2. All banks have the same requirements.

3. We obtained the best possible purchase prices.

4. All insurance companies have the same rates for all individuals.

5. The loan will be approved, no questions asked.

6. There will be no major mechanical problems not covered by the warranty (for the two dealership cars).

7. The cost of any major mechanical problem on the used car without a warranty will not exceed $1400 for the first year.

8. Total miles driven will be low enough so that no more than four oil changes will be needed in the first year.

9. We cannot accurately estimate gas expense since we have not been licensed drivers for long and also because this is our first car (at least not without making numerous assumptions).

10. We have covered all possible expenses for the first year.

The three cars we have researched are : 1) a new 1993 Plymouth Sundance; 2) a used 1991 Pontiac Sunbird; and 3) a used 1987 Ford Tempo. Randy Berck from The First National Bank helped us determine our loan information for each of the cars. Heather Green with USAA Insurance quoted insurance prices for us. Betty Richards from the BMV helped us gather information on plating and titling the cars.

The following is the data we have collected on the expense of owning each of the three cars.

**1993 Plymouth Sundance**, from Alberts Chrysler-Plymouth with a purchase price of $9463.00 and an average of 32 mpg.

__loan information__ ! the amount to be borrowed is $8000

! with an 8.0% interest rate

! for a period of 48 months

! and monthly payments of $194.63

__title and plates__ ! $5.00 one time title fee

! $256.65 plate fee for the first year

__insurance information__ ! $375.80 every six months

! full coverage

! deductible of $500.00

__mechanical expense__ !$21.95 for oil change every three months (Goofy Oil Changes)

! all other expenses covered under a three year warranty

1991 Pontiac Sunbird, from Polar Chevrolet-Pontiac with a purchase price of $8795.00 and an average of 26 mpg.

__loan information__ ! the amount to be borrowed is $7200

! with a 10.0% interest rate

! for a period of 48 months

! and a monthly payment of $182.15

__title and plates__ ! $5.00 one time title fee

! $217.85 plate fee for the first year

__insurance information__ ! $335.59 every six months

! full coverage

! deductible of $500.00

__mechanical expenses__ !$21.95 for oil change every three months (Goofy Oil Changes)

! all other expenses covered under a one year warranty

**1987 Ford Tempo**, listed in classified ads (Scott Hayes, telephone 721-4761) with purchase price $1100.00 and an average of 21 mpg. We decide to use only $100.00 from our savings and keep the remaining savings as a "cushion" in case of any major mechanical problem(s). Therefore we are considering this to be a trade off, a monthly car payment for monthly mechanical expenses.

__loan information__ ! the amount borrowed is $1000

! with a 12.5% interest rate

! for a period of 12 months

! and a monthly payment of $93.00

__title and plates__ ! $5.00 one time title fee

! $186.25 plate fee for the first year

__insurance information__ ! $297.99 every six months

! full coverage

! deductible $500.00

__mechanical expenses__ !$21.95 for oil change every three months (Goofy Oil Changes)

!all other charges will be taken care of by money in the savings account ($1400.00 unused)

Now for the weekly expenses for each of the three cars.

**Sundance** car payment $48.66

title/plates $05.03

insurance $14.45

__oil changes__ __$01.69__

TOTAL $69.83

**Sunbird** car payment $45.54

title/plates $04.19

insurance $12.91

__oil changes__ __$01.69__

TOTAL $64.33

**Tempo** car payment $23.25

title/plates $03.68

insurance $11.46

__oil changes__ __$01.69__

TOTAL $40.08

Note, we did not add gas expense in for two reasons. First, any figure we used would be pure guess because this is our first car and we are newly licensed drivers. At this point we are very unsure of the number of miles we will be driving, but we will be driving to work, running errands for mom and dad, toting friends and siblings around town, and what ever else might come up (we could really accumulate a lot of miles). Second, and probably most important, the upcoming graph does take into consideration gas expense and our analysis will be based on this graph.

We will now develop our cost-mileage equations for each of the three cars and then graph them on one set of axes.

We watched gas price for a period of one week and then took an average of those prices. Our average gasoline price for the week is $0.979 per gallon. In each of the cost-mileage equations we let x represent the number of miles driven and y represent the total cost (including gas) of running each car when driven x number of miles. In calculating each car's total cost (y) we divided cost per gallon of gasoline by mpg for each car, multiplied the result by miles driven (x), and add in the total weekly expense of each car (figured above).

**Sundance** y = __.979__ x + 69.83

** ** 32

**Sunbird** y = __.979__ x + 64.33

26

**Tempo** y = __.979__ x + 40.08

21

Recall: x = # miles driven and y = total cost including gas

As we look at the expenses for each car and the cost-mileage graph we decided the Tempo would be the best choice under the constraints we are working with. According to our graph the Tempo is the most economical choice, unless we were going to drive in excess of 1875 miles in a week (realistically we know this is impossible for us to reach). Another reason we like the option of the Tempo is because of the way we are handling our savings account. Since we chose not to use the savings account as a down payment it left us with a safety net. We are aware that this could blow up in our faces if the car ends up breaking down every other week or so.

An interesting point to note from the graph is that the new car is not always the most expensive. At approximately 750 miles the new Sundance becomes less expensive for us to own and maintain than the used Sunbird (although it is still more expensive than the used Tempo). Therefore, if we were trying to decide between the Sunbird and the Sundance we would really need to estimate the number of miles to be driven in an average week. As we examined the graph further, we noted that the Sunbird is never the most economical.

**Evaluation Guidelines:**

research and documentation 10 points

presentation 10 points

equations, graph, and analysis 15 points

__style, format, and clarity__ __05 points__

**TOTAL** ** 40 points**

**Extensions:**

1. Delete financial resources and give a "typical" month=s working schedule and per hour wage.

2. Have students randomly select a crisis to deal with, i.e. accident, illness and loss of job for a week, traffic tickets and increased insurance rates, car theft, etc.

3. Look at expenses over a given number of years.

**Wheeling Deals**

**ALL** the expenses of owning and maintaining a car for the first year.

*Funded in part by the National Science Foundation and Indiana University 1995*