CAR Archives | Math for Grownups

Earlier this week, we took a look at one of the big personal finance decisions out there–buying a car. But the price of the vehicle alone isn’t the only consideration. Unlike a blender or sofa, your shiny new mode of transportation will tap your budget year round. But by how much?

Generally speaking, car ownership involves four additional costs: fuel, maintenance, insurance and taxes. (Some states and municipalities don’t have a property tax on vehicles, so you might be off the hook for that last one.) Problem is, these costs aren’t like your mortgage or cable bill. They can be hard to predict and aren’t due at the same time each month.

So how can you plan for these? Well, just like any other irregular or unexpected costs, it’s a good idea to put something away each month for car expenses. The trick is figuring out how much you’ll need. Let’s start by estimating the annual costs for each of these items.

Fill ‘er up

With gas prices rising and falling like the barometric pressure on a spring day, budgeting for fuel sure ain’t easy. But you can get a rough idea of what to expect, and then tweak that amount as the year goes on.

You’ll need to consider several variables for this one: the miles you travel in a given year, your vehicle’s miles per gallon, and the cost of gas where you live. This is going to be an estimate, of course. Unless you’ve got a wicked crystal ball, you won’t be able to predict any of this for sure–but you can get close.

If you’ve been keeping records of your miles traveled, you can take a look at the previous year to predict this number. Of course if you’re like me, those records don’t exist. So figure out a rough estimate based on your commute (if you have one), annual trips and even carpool. You should add on for errands and other around-town trips. For reference, the U.S. Department of Transportation estimates that on average, Americans drive 13,476 miles per year.

Now calculate the amount of gas you will likely consume. Let’s say your car gets 32 miles per gallon, and you expect to drive 14,500 miles this year. To find out how many gallons of gas you’ll use, divide:

14,500 ÷ 32 = 453.125 gallons

And the last part is simple: multiply this number by the cost of gas per gallon. In my area, we’re averaging about $3.85 per gallon, so for the sake of this example, let’s use that number.

453.125 • 3.85 = 1,744.53

The annual cost of gas for this fictional vehicle is estimated at $1,744.53.

Maintenance and Repairs

While maintenance can be pretty predictable, repairs are something that you can’t foresee–just like you didn’t see that light pole behind you in the Giant parking lot. But you can budget for these.

Again, if you keep good maintenance records, you can review these to see what you have paid in past years. Your mechanic may have these on file, as well. Remember, most maintenance is based on the number of miles driven, so if you add a long commute, you can expect these costs to rise. The kind of car you drive also matters. And of course, older cars will likely require more maintenance and repair.

If you haven’t tracked these expenses, you will probably have to make a good guess. Ask your dealer or mechanic about this. Or start with $2,000 per year and see what you have left over in December.

Whatever you do, don’t forget your Emergency Fund. This is where you’re big, unexpected repair costs will come from, like an accident that isn’t covered by insurance.

Speaking of Insurance

If you’re driving in the good old U. S. of A. and you don’t have “Farm Vehicle” stamped on the bumper of your truck, you will need to pay insurance. Again, this is a cost that depends on several variables, including your age, your driving record, and much more. But once you choose your insurance policy, that number will be set in stone, as long as you keep your driving record squeaky clean.

The Tax Man

Some states (and some municipalities) require personal property taxes on vehicles. Problem is, these payments are not usually monthly. Sometimes they are only charged annually, and in some places, residents pay these taxes quarterly.

To budget for taxes, take a look at what you paid last year. Or look up a property tax calculator for your state.

Month by Month

Let’s say you’ve found all of these annual costs. Now it’s time break them down, so that you can put away some cash each month.

Fuel = $1,744.53 per year

Maintenance = $2,000 per year

Insurance = $1,566 per year

Taxes = $2,867 per year

First add these to find your total annual costs:

1,744.53 + 2,000 + 1,566 + 2,867 = $8,177.53

Now divide this total by 12 to get your estimated monthly costs.

8,177.53 ÷ 12 = $681.46

So, based on this fictional numbers, socking away $682.46 for car expenses should cover the annual cost of owning and maintaining this fictional car. (Your milage may vary.)

Do you have any tricks for covering these unpredictable costs? Share your ideas or questions in the comment section.

When you’re looking at your personal finances, the big expenses stand out. That means purchasing a car is a huge consideration, and deciding between new and used can make your mind turn to mush. Do dealer and automaker incentives–like free financing or cash back–make a big difference? Sometimes yes, sometimes no.

Today, I’m bringing you an excerpt from my book, Math for Grownups. Use this math, and you can make an educated vehicular purchase, speedy quick.

Used cars are generally less expensive than new ones, unless you’re deciding between a pre-owned Hummer and a brand new Hyundai, of course.

But how do dealer and automaker incentives stack up to buying used?

Check it out!

Roxanne is trying to decide between two cars. Her local dealership has a current model priced at $25,000, including tax. But online she saw the same car—pre-owned—for $15,000. The used car is in excellent condition and certified. Plus, the warranty transfers, so price is her only real consideration.

The dealership is offering free financing. And the automaker has a $2,000 cash-back program. That means she’ll pay exactly $23,000 for the car and no interest at all.

But to finance the used car, she’ll have to get a loan. To compare the prices, she’ll need to find out how much she’ll pay in all for the used car. That means she needs to know what interest on a loan will cost.

In order to calculate that, she’ll need to know the principal (the amount she is borrowing and the basis of the interest calculation). That means the principal is $15,000. She’ll also need to know the interest rate. Her bank is offering a 6% interest rate on car loans, for a period of 4 years. The interest is compounded annually, so once a year, the interest rate is calculated and added to the loan amount. Thus compounding interest means that in every year for the term of the loan, except the first year, Roxanne is paying interest on the interest she paid the year before (and the year before that . . . and you get the idea).

Roxanne can use an online calculator, or she can turn to a really simple formula:

A = P(1 + r)ⁿ

Okay, breathe. It only looks hard. It’s not difficult at all if you remember the order of operations—that is, what you do first, then second, and so on.

First, do anything inside the parentheses. Next, take care of exponents—those are the little numbers at the right top of another number. They tell how often to multiply the bigger number by itself. (Thus 4²means 4 4, and 16⁵ means 16 16 16 16 16.) Then multiply or divide. And finally, add or subtract. In other words, Please Excuse My Dear Aunt Sally, or PEMDAS:

Parentheses
Exponents
Multiplication
Division
Addition
Subtraction

Ready to apply this formula? With PEMDAS, you can do it!

A is the total amount she’ll owe

P is the principal

r is the interest rate per compounding period

n is the number of compounding periods

Roxanne’s principal (or the amount she’s borrowing) is $15,000, so P = $15,000. Her interest compounds yearly, so her rate is 6%. To make it easier to multiply, she can convert that percent to a decimal: r = 6% = 0.06. And because the compounding period is annual, and the length of the loan is 4 years, n = 4.

A = $15,000(1 + 0.06)⁴

First add the numbers inside the parentheses.

A = $15,000(1.06)⁴

Now calculate the exponent. Remember, 1.06⁴ = 1.06 • 1.06 • 1.06 • 1.06.

A = $15,000(1.26)

Last step! Just multiply.

A = $18,900

So, Roxanne would pay $18,900 total if she finances the purchase of the used car.

That’s a heck of lot less than the $23,000 she’d pay for the new car. And she hasn’t even figured in her down payment yet.

Why does that change anything? Because after making a down payment, she would be paying interest on less principal (remember, that’s the amount she’ll be borrowing). How would a $1,500 down payment affect her decision?

For the used car, she’d finance $13,500 instead of $15,000.

A = $13,500(1 + 0.06)⁴

A = $13,500 • 1.26

A = $17,010

So the total she’ll pay for the used car is $17,010.

And for the new car? She just needs to subtract her down payment from the adjusted price: $23,000 – $1,500, or $21,500.

Judged on the basis of price alone, the new car doesn’t seem so minty fresh.

Do you have questions about using this formula? What about questions about buying cars and fitting the payments into your monthly budget? (On Friday, I’ll talk about the year-round cost of owning a car, a consideration that is critical at the buying stage. And later this month, we’ll take a closer look at compound interest.)

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