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# How Basic High School Math Can Make You a 401k Millionaire

Think back to your high school math days. Inevitably, some student at some point in a math class (usually algebra) asks, “Are we ever gonna use this stuff in real life?” Good math teachers pounced on that one to present real-life applications that inspired their students to use their math knowledge to get ahead in life. Unfortunately, a lot of today’s workers must have been daydreaming during that discussion, because looking at our retirement saving behavior as a nation, we missed that math boat.

Some professors at UC San Diego ran an experiment on about 100 college students to see how well they understood the idea of compound interest. What they discovered is that many students don’t understand the difference between exponential growth and linear growth. Exponential growth is the power behind compound interest. In simple terms, it’s the idea of not just earning interest on a deposit, but also earning interest on the interest, again and again over time. Linear growth, on the other hand, is simply the idea of earning interest one time on a deposit.

In real life, exponential growth is what a typical American worker experiences by saving for retirement through a 401k or 403b retirement plan at work. Month after month, a small amount of a worker’s paycheck is put into a retirement account. Once there, those investments (hopefully) grow over time because of the worker’s wise investment choices. But based on the professors’ experiment, it seems most workers think linearly instead of exponentially.

For example, let’s assume you invest \$1,000 per year for 10 years and earn a nice round 10% return every year. How much will you have after 10 years? In the experiment, the college kids basically figured 10 years times \$1,000 equals \$10,000, and 10% of \$10,000 is \$1,000, so you end up with \$11,000. That’s linear thinking. But if you understand compound interest, or the idea of exponential growth, the true answer is almost \$16,000, a difference of nearly \$5,000!

What does this mean? Because we linear-thinking workers don’t understand exponential math, we delay saving for retirement. We don’t see the cost of waiting to save. The example here was for 10 years. Imagine how mega-underestimated the answer might be for a 30- or 40-year period of time, which just happens to correspond to the typical worker’s time to save for retirement in their 401k. Is it then any wonder we tend to put off saving for retirement? Why oh why didn’t we pay closer attention to those little exponents in high school??

Now to the millionaire reference in this article’s title. Let’s assume the average car payment in the US is \$350, and you begin your working career by age 25. You’ll work to age 65, for a total of 40 years. If you put away a car payment into your 401k retirement savings every month for 40 years, what kind of interest rate do you need to be a millionaire by age 65? 7.5%. And that rate of return is certainly do-able over 40 years, even including bad investment decades like the 2000s. If you only earn 5%, by the way, you’d wind up with “only” about a half million for retirement. Not bad for a car payment.

Linear thinkers: wake up! The power of the exponent. The power of compound interest. We all learned about it in high school. How quickly we forget. It costs our retirement accounts—a real life application of basic high school math. If you want to be a millionaire at retirement, you know what you need to do.

Comment   |   Share This Guide   |  Mar 29, 2012 from Orland, IN