James Clear, in his bestselling book *Atomic Habits*, provides a thought-provoking illustration: Suppose a plane takes off from Los Angeles on its way to New York. But, after taking off, the pilot turns the nose of the plane by an almost imperceptible 89 inches. Where will the plane end up? The answer: nowhere near New York. As it flies across the country, that 89-inch difference will take it hundreds of miles off course.

Clear’s purpose in providing this illustration is to help readers appreciate a concept that is difficult for the human brain to grasp: It’s called compounding. The idea, if you’re not familiar with it, is that repeated actions build on each other to produce results that are dramatically larger than one might expect. A common and entertaining example is this: If you were to take a piece of paper and fold it in half and then fold it in half again, and do that 40 more times, it would grow so high that it would reach the moon. Continue folding that piece of paper just nine more times, and it will reach the Sun.

Another common example: Suppose you started with one penny on the first day of the month and then doubled it each day—to two cents, then four, then eight, and so forth. The results are similar to the paper experiment: After ten days, you’d have $5. After 20 days, you’d have $5,000, and after 30 days you’d have more than $5 *million*.

While entertaining, these examples are so extreme that they are of little practical value. But they carry an important lesson: The path to improvement in any domain does not require swing-for-the-fences, Herculean efforts. It requires only small steps done consistently. This is the meaning of “atomic habits.”

The problem, though, is that we’re just not very good at doing compound calculations in our heads; we tend to think more linearly. Ask people to guess at the paper folding question, and typical answers will be in the range of three feet. And answers to the penny question normally fall in the range of a thousand dollars. Unless you work out the math step by step, it’s very hard to make an estimate that’s anywhere close to correct.

The result—because the human brain isn’t wired to think in compound terms—is we believe we have to take dramatic steps to see any progress at all. That’s why, in my opinion, things like the keto diet are all the rage—why aim for a lowly goal like losing a pound a week when you could shed fifty pounds in a matter of months? Or, in the world of personal finance, that’s why it’s common to see magazine covers promising, “137 Ways to Get Rich” or “8 Stocks to Buy Now!” Get-rich-quick schemes appeal to people not because they’re lazy, in my opinion, but because they don’t appreciate the reliable math behind a get-rich-*slowly *approach.

How can you apply the power of compounding to your personal finances? Here are some ideas:

**If you’re early in your career and not saving at all**, start with the smallest possible contribution to your 401(k), perhaps 1%. You’ll barely feel it, and at first the progress will seem minimal. Indeed it *will be *minimal. But don’t get discouraged. That’s the tricky thing about compounding. At first, the results will seem incredibly slow, but eventually they start to snowball—just like that penny that grows from $5 in ten days to $5,000 in twenty days. The key is to keep going even when it feels like you’re not getting anywhere.

**If you have a high income, you might think it’s not worth contributing to a Roth IRA. **As you may know, high income individuals aren’t eligible to contribute directly to Roth IRAs and must follow a two-step process. With an annual contribution limit of just $6,000, you might think it’s not worth the administrative effort to make these contributions. But consider this example: Suppose you’re 35 today and married. You’ll be able to contribute a combined $12,000 into Roth IRAs and increase those contributions modestly over time as the limit increases. If you do that every year until you’re 65 and earn 7% average returns, you would end up with more than $1.5 million by age 65. So don’t think about it as “just $6,000.” Think about it as potentially $1.5 million.

**If you have children in college and are paying astronomical tuition bills, **you might feel like it’s not even worth the effort to economize, that any savings will be just a drop in the bucket. But consider this example: Suppose you’re 45 years old, and your first child is entering college. And let’s say your child is considering two private schools, each charging about $70,000 per year, but one offers $5,000 in aid. At first, that might seem like an insignificant difference. But that ignores the value of compounding. If you shaved $5,000 off your tuition bill for four years and earned 7% returns on your savings, you’d end up with $100,000 by age 65. Yes, $5,000 might seem like a small difference in the context of the enormous bills you’re paying, but don’t think about it that way. Look at it as $100,000. And remember, private colleges are businesses and are perfectly willing to negotiate aid packages. They won’t advertise that fact, but they most certainly are.