Let's Make a (Car) Deal!
“Let’s Make a Deal” was the name of a TV game show that began in 1963 and lasted for over two decades. It was best known for what came to be called the “Monty Hall” problem that captured the counter-intuitive nature of probability.
What interests me here is showing how to calculate in your head the approximate monthly payment you will have to make on a car, given its price and the interest rate applied in financing it. (The assumption is that you are not paying full price at the time of buying. Most of us don’t have that much cash, true for maybe 99% of the population!)
Of course, the salesperson selling you the car will tell you what your monthly payment will be. Because most of us think that this calculation is beyond our ability, we meekly submit to whatever the salesperson says. It doesn’t have to be that way. There are some simple calculations you can make in your head that will tell you whether you got the best possible deal when buying the car of your choice.
Let’s say you are buying a car that costs $28,000. You put $3,000 down and finance the remaining $25,000 (principal) at an Annual Percentage Rate (APR) of 4% over 5 years (60 months), the term of the loan. What will be your approximate monthly payment?
To get an estimate of the lowest possible payment, that is, without any interest, simply divided 25,000 by 60 months. Six goes into 24 exactly 4 times, so for $24,000, it will be $400. To account for the remaining $1000, increase $400 to $420.
Now comes the correction for the APR, the interest you will have to pay on the loan. All such loans are compound interest loans, that is, you will have to pay interest on interest. To keep things simple, let’s assume it is simple interest in which the total amount you pay due to interest is fixed. (For compound interest, it is the APR that is fixed while the interest amount varies).
The total amount of simple interest in this case = 4% of 25000 for 5 years = (0.04 x 25000 x 5) = 5000. (Notice that 5 x 0.04 = 0.2, which is 1/5, and a fifth of 25000 is 5000.) So the total cost of the car over 5 years is $25000 + $5000 = $30,000. If you divide $30,000 by 60, (easy because 6 goes into 30 exactly 5 times), it comes to $500.
How much more does compound interest add to the monthly payment? If you were to do the formal calculation, it comes to about $510. So the ballpark figure of $500 comes pretty close! You can simply add $20 to $50 dollars to account for the compound interest. In other words, the minimum amount (no interest) is about $420 and the maximum is about $550.
By doing this type of approximate calculation in your head, you not only convince the salesperson that you are a savvy customer, you also become better at dealing with numbers. This can only help, sometimes in big ways when someone is trying to pull a fast one on you!
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Hasan Z Rahim
Hasan Z. Rahim is a professor of mathematics and statistics at San Jose City College,
located in the heart of Silicon Valley, California.