Cars are a source of pride, embarrassment, and envy, as well as transportation. This opening
discussion allows the class to get their desires on the table as well as more practical
interpretations of the word "ideal". The class could make a list of the attributes they might
want the ideal car to have.
The vehicle ownership, purchasing and leasing report has a great wealth of statistics and vocabulary, which could lead to much discussion.
You might consider asking the students to guess about the cost of various cars. They might be surprised as the discussion unfolds
.
- The discussion here should end up including some practical things, such as the longevity of
the vehicle, its safety, and its repair record. Why, for example, does a certain brand have a
good reputation? What will you use the car for? What must you carry in the car? Where will you park the car?
- The question about values encourages a broader discussion of things like environmental
impact. The question of whether a hybrid vehicle or an electric car is a good "deal" could
be the subject of an independent investigation by one or more students, although it is not
included directly in this module.
- "What will make you happy?" is designed to open a discussion about needs versus desires.
The list of desired traits in a car should be divided along these lines.
- It is perfectly ok if the students pick unreasonably expensive cars, as long as they
discover at the end of the module that they have done so.
- It would be great if the range of cars chosen by the class includes very expensive to
very cheap options, as well as many in the middle. This would make the class discussion
much richer as the module progresses.
- Encourage the students to use the car sites to get information on longevity, repair
records, etc. as well as just the expected price.
- A comparison of two cars across a variety of features would make a good short writing
assignment.
- You can get true cost to own on Edmund's and 5 year ownership costs on Cars.com. This includes all the expenses that are discussed on the next slide.
- Insurance quotes can take a small amount of time to obtain, so plan accordingly. If students do not want to enter personal information, they can obtain an estimate from Edmunds or Cars.com, which basically lay out the five year costs for each vehicle. They obviously just make assumptions and give averages but they are faster.
- It would be worth considering the difference in insurance cost if you add a student to
a parent's policy. This is an estimate the parent can obtain.
- This discussion also provides an opportunity to invite a local insurance representative
to class for a more complete discussion of options.
- Remember also that the kind of coverage necessary will depend on whether there is a
loan involved, so the initial cost will determine that.
- A list of expenses related to car ownership might include:
- Insurance
- Repairs
- Registration
- Gas costs
- Longevity
- Warrantees bought separately
- Resale value after a certain time (depreciation)
Students could create a spreadsheet to track these, although a list will serve as well.
- Maintenance
- Financing
For the Future Teacher
In courses where the enrollment includes, or is primarily future teachers there are
several ways this module can be extended to encourage connections with the elementary curriculum.
The initial cost and recurring expenses of buying and owning a car are similar to the
issues involved with purchasing and owning a pet. Whether it is a lizard, a dog, or a pony,
many of the same issues are involved and could be the basis for a rich lesson for the
elementary level. Have your students design a lesson or an integrated unit for an
elementary classroom on researching, budgeting for, and owning a pet. They should consider
issues such as feeding, boarding, veterinary expenses, grooming, special housing or
equipment, unexpected expenses such as new rugs or scratched doors, as well as the
emotional aspect of choosing a pet.
Some inspiration and resources:
VIDEO: The Joys and
Rewards of Small Pet Ownership.
VIDEO: Responsible dog
owner day American Kennel Club.
ASPCA
cost of ownership.
VIDEO: The Chewinator.
VIDEO: Bad dog.
This calculation is a good exercise in basic quantitative literacy. Depending on the
students, the instructor might want to skip the scaffolding and just ask the final question:
what is the yearly cost of gas that you expect? The students could figure out how to answer
this question themselves. This alternative would be preferable to the leading questions we
have provided. These questions could be shown after the students have made an attempt at it,
possibly leading to a revised estimate.
Please have your students watch and discuss this video. Colleen Andrasko, the
speaker in the video, describes two different car purchases and the financial
implications of each of them. You are giving your students the opportunity to
make the same choices or mistakes, in advance of purchase, on paper. This is exactly
what quantitative skills are about. But these stories might bring up other aspects
of car purchases not so far considered. By the end of the discussion, your students
should also be considering:
- Risk -- of missing payments, of the car having a shorter life than expected, etc.
- Household budget-- and what percentage of it should be devoted to maintaining and financing
the car.
These will eventually be points of comparison for the various cars studied.
The idea of repossession and implications for credit score could be a separate discussion, as well as the role and responsibility of a cosigner.
There is a spreadsheet that calculates both the amount due on the loan
every month and the value of the car after depreciation. There is also a
worksheet to guide student calculations.
- If you don't want to use a spreadsheet to do interest and payment calculation,
cars.com has
several calculators that do the same thing.
-
Moneyzine has a car depreciation calculator if you don't want to use the spreadsheet for this.
- However, only the spreadsheet allows you to see the relationship between the two over time.
This is an interesting relationship, because there is often a period during which the value of
the principal remaining to be paid in the loan exceeds the resale value of the car. Usually
if you have to sell the car at that point, you will make less on the sale than you owe, creating
a financial risk. So it is really better to use the spreadsheet now in order to have that
discussion later.
This slide asks students to consider the monthly cost of the car in two ways. One is in absolute
terms (the total monthly cost of the car, insurance, etc. over five years of ownership). The
other way is to subtract the resale value of the car at the end of that period and prorate it
over five years, subtracting the result from the expense.
Here are some discussion questions:
- What are the relative merits of these two ways of calculating costs? Which is more relevant
to your situation?
- Which of your cars did better in these two calculations? See if anyone in the class had a
situation where one car did better than the other when expense was calculated without resale
value, but worse when resale value was taken into account.
- The resale value of a car stems from depreciation. The value of the car decreases by a
percentage every year. What kind of growth is this? (answer: exponential growth, with a
negative exponent, or exponential decay) This is a good moment to tie the discussion to previous mathematics content.
- One version of this exercise is to have student choose the “car of their dreams” and then, by contrast, the “practical car” they believe they can afford. Sometimes the car of your dreams is a better deal if you sell it after paying off the loan, because depreciation is low compared to a cheaper vehicle. Thanks to Clyde Martin of Texas Tech University for this example, which he uses with his college algebra class.
For the Future Teacher
The topic of Interest rates provides an opportunity for future teachers to discuss how the
concept of compound interest, both negative for a loan and positive for savings, can be
introduced into the classroom.
Percents are part of the middle school mathematics curriculum and this is where the concepts
of simple and compound interest are sometimes first introduced.
For those who are not yet ready for algebra, the concept of exponential growth can still be
explored efficiently by having students use a calculator and repeating the multiplication of,
for example, 1.04 (for 4% growth compounded annually or .96 depreciation per year compounded
annually) to watch how the initial amount will change over time. This could be followed by a
class discussion about why their parents use a bank instead of keeping their money in a
mattress. Which would the class rather use for their own money? Have your students design
a lesson for the classroom or give them a short writing assignment describing how they could
introduce the topic of compound interest.
The business of "upside down" car loans is the basis for a rich discussion. Here are some
questions to help guide that discussion.
- Who had car loans that were upside down for some period? (List types of cars and loans on
the board.) What changes could be made to the loan if we didn't want this to happen? (Bigger
down payment, lower interest, cheaper car, shorter loan, etc.)
- What is the problem with an upside down car loan? The students should be able to figure
this out: risk. But there are two kinds of risk. Students are likely to identify the risk
that the borrower cannot pay the loan (due to job loss, for example, or unforeseen expenses.)
and has to sell the car and take the loss. The other sort of "risk" is that
the borrower may have increased resources, and want a better car. Although this is a "want"
rather than a "need", it can still occur. In either case, the borrower will lose money.
- At this point it is interesting to ask this question: What is really being sold to the
consumer, the car or the loan? Did the car dealer make more money on the markup from
wholesale to retail, or more money on the interest on the loan?
These short clips reinforce the explanation of the "upside down" loan in both technical and
personal terms. You might have a discussion along the following lines:
- Is it a terrible thing if the loan is "upside down" for a while? If so, why do lenders
agree to give such loans?
- You want to drive home the observation that the level of risk depends very much on how
easily the car expense fits into the household budget.
- This is a place to discuss what can happen when the budget is too tightly constructed.
In the previous video by Colleen Andrasko, the second scenario where her niece defaults on her
car loan is most likely an example of a too tightly constructed budget. One unexpected large
expense can turn a positive monthly cash flow into a negative cash flow
that feeds on itself.
- So the question "Which car can I afford?" depends on our ability to estimate our other
expenses as well.
Here we are giving the students a chance to budget on a large scale. Most younger people are
not really aware of what stuff costs: the apartment, the electricity, the heat, etc. We
suggest the following strategy.
- As a class, make a list of all household expenses.
- Give small groups one of these expenses to estimate. For example, a group could contact
the local energy company for data on electricity usage and rates over time. Each of these
estimates should be presented in written form with supporting data, for the rest of the
class to use. In the interests of quantitative literacy, we should make every excuse to
have students write about calculations and data.
- Putting all of this information together will give an estimate for a household budget.
Individuals can then estimate their income based on their expected job, use the group
exercise to estimate other expenses, adjust these based on specific decisions (such as
taking roommates, for example), and see how much is left to spend when the needs are met.
The main question then becomes: How much should be left over for unexpected expenses?
For the future teacher
Children are often interested in starting businesses, selling balloons, lemonade, berries
or services such as mowing lawns. Budgeting for a small business would be a natural way
to introduce this topic to the classroom as there are many costs children will not have
considered to be part of a business. Have your students choose a business and make a list
of all the expenses related to starting that business. How much capital will be required?
Will a parental loan be necessary? How much money will they have to make to make a profit?
Here is some inspiration:
How to start a
lemonade business.
Hunter
and Gunnar's lemonade stand.
Learning business
through Lemonade.
After your students have listed the costs for starting a business have them design a
budgeting lesson or unit that they would use with their students.
When students are listing things they could do with the extra money, it is good to make
sure that saving it is one possibility. What can be done with an extra $40 saved every
month over five years? That depends on the interest rate you might get, but it does
compound over time.
Bankrate has a savings calculator that students can use to figure out the opportunity cost. Assuming
$40 per month (for example) at 4% interest (again, for example), over the course of 5 years
of car ownership, yields $2,700 in savings. This is one way to measure opportunity cost.
The module ends on a humorous note. We know the second video has poor quality, but it's worth it.