“Car designers are just going to have to come up with an automobile that outlasts the payments.”
–Erma Bombeck
It seems that every time I turn on a Fort Worth radio station, I hear advertisements for car dealers. Never, ever do I hear those advertisements talk about the price of a car. Have you ever heard a car advertisement saying “You can get a new car for as low as $24,999!”???
What do you hear instead?
“Payments as low as $249 a month!”
They’re playing a trick on you and taking advantage of a hole in Monkey Brain’s thinking.
Let’s take a little test. It’s hypothetical, but stick with me.
Let’s imagine that you’re buying a car. The car costs $10,000, but you finance it with the dealership. You’re going to make 12 monthly payments of $1,000 each and have the loan paid off in a year.
What’s the interest rate on that loan?
Take a second.
Now, let’s keep reading.
If you’re like most people, you answered 20%.
The answer?
35.1%
If you thought the rate was 20% or lower, then you’ve fallen for a common trap that Monkey Brain falls into all of the time called the exponential growth bias. First explained by Dartmouth’s Victor Stango and Jonathan Zinman, the exponential growth bias means that we’re more likely to underestimate costs of short-term borrowing and overestimate the present value of money compared to its future worth.
Before we look at how this bias can affect your finances, let’s look at why it happens.
For those of you who are new here, our brains have two main components. There’s the prefrontal cortex, or the thinking you. It’s refined. It thinks of the future. If you’re having thoughts right now, then it’s probably due to the prefrontal cortex. That Thinking You is the one who pushes you away from the dinner table when you’re full rather than ordering a double banana sundae even though it sounds really good.
The other part of our brain is the limbic system. It’s the brain structure that got us through caveman days. When we saw a woolly mammoth, we didn’t have time to contemplate its beauty, consider whether or not it had feelings or a family of little woolly mammoths back home, or enjoy the play of light against its fur. Instead, we had to decide: run or attack. The ability to make a rapid and correct decision determined whether or not we had dinner, were dinner for the mammoth, and lived to see another day. Thus, our brains needed to be quick and decisive, and emotions ruled the roost. Fear? Run! Hunger? Hunt!
We share the limbic system structure with monkeys, which is why I call the limbic system Monkey Brain. Monkey Brain doesn’t like to think about the future, because, after all, when you were a caveman, your future horizon was very short. You were concerned with eat or be eaten decisions, not what you wanted your cave to be decorated with in 30 years’ time. So, too, it is with Monkey Brain. He wants pleasure now, and will gladly sacrifice your retirement account for a man cave or Jimmy Choo shoes right now.
Thus, because of Monkey Brain’s tendency to overvalue the present and discount the future, it’s easy for him to come up with alternative explanations.
You: “Paying $2,000 in interest in one year for a $10,000 loan is pretty expensive.”
Monkey Brain: “STUPID HUMAN. 2,000 DIVIDED BY 10,000 IS 20%. EVEN MONKEY KNOW THAT MATH. HUMAN DUMBER THAN MONKEY BRAIN.”
You: “Oh yeah. You’re right! Get a pen so I can sign this loan paperwork!”
Any time we have potential exponential growth, that’s hard for Monkey Brain to handle. There are squares and powers and all of those tough math issues that Monkey Brain doesn’t like to deal with. So, he’s going to try to make things as simple as possible for him to wrap his little monkey head around. To do so, he assumes linear math instead of exponential math, which is why you most likely thought that the interest rate was 20% instead of 35.1%.
Why did the article not explain the math behind why it was 35.1%? It seems like it was a perfect opportunity to show people why it isn’t 20%.
Solving for the rate involves reasonably complex algebra (see this explanation of the formula for amortized interest for an example), and arriving at a formulaic answer is tedious.
The better approach is to set up a formula in either Excel or a Google spreadsheet.
Set cell A1 to equal the interest rate
Set cell A2 to equal the number of months: 12
Set cell A3 to equal the amount: $10,000
In cell A4, enter the forumla =PMT(A1/12,A2,A3)
Then use goal seek to set A4 to equal -1000 (the payment) by changing cell A1.
The actual answer is 35.0742%.