As a private Math tutor, my students often ask why or when in the real world, they will ever need the math skills they’re required to develop in middle and high school. The example below seems to work and gets their attention.

So you want to buy a new car someday? Better start saving up, and here is why:

Let’s say you decide on the most practical and popular car sold in the USA, a Toyota Corolla with an MSRP around $21,000. We all know there will be additional costs that could jack that price up by a couple thousand more, but for this example we can use the MSRP. You might think that is a lot of cash to save, so you look into a car loan.

While doing some research you learn that most dealers require a down payment. A good thing you banked $1,500 from the lifeguarding job you had last summer between your Junior and Senior year. Plus, now that you have a regular part time job at Petco grooming poodles, you can actually qualify for a loan so long as your parents co-sign.

Since your parents agree to co-sign, the dealer offers you a killer loan – with an annual interest rate of 5.75% for 60 months. Of course the dealer wants to sell you the car based on a monthly payment and convince you to purchase additional options – “Bluetooth hands free will only cost you an addition $8/month, you’ll also want the Navigation and color display I showed you during your test drive for another $22/month.”

You figure since you’re financing the car anyway, what’s a couple extra bucks a month? Besides, you love the candy apple metallic red with cream faux leather interior. With mom and dad on the sidelines wishing your experience at the dealer will serve as an education you begin to wonder how much this car is actually going to cost you.

A nagging memory from 11 grade algebra comes into play because you recall there is a quick and easy way to do the calculation, but you don’t remember the formula. So in case you read this article before shopping for a car, here’s a quick review:

The exponential growth model is an excellent tool to file away in your memory. Hopefully you’ll use it so often that it will immediately come to mind anytime a credit card application arrives in the junk mail.

Base x rate with an exponent the value of the time interval. In this case you will be financing $19,500 at 5.75%, 60 months translates to 5 years, so that will be your exponent. Your formula and result will look like this:

$19,500 x 1.05755 = $25,689

That doesn’t even include the down payment! Oh and the monthly payment is what now? $418 per month? Are you going to have enough left over from your part time job to maintain your nice new car, put gas in it, be nice and offer to pay your parents the add on to their insurance policy?

Your mom and dad are pleased when you realize the car will actually cost you more than $6000 above the price advertised. When you leave the dealership with your parents but without a new car, your dad says he’ll give you an interest free loan and help you find a safe/reliable pre-owned car for close to the amount the interest you’d have had to pay if you’d financed a new car.