Jonathan Clements | October 14, 2015

**A GOOD GRASP** of compounding is fundamental to managing money. Without an understanding of the way money grows and shrinks over time, folks can’t fully appreciate the value of starting to save when they’re young, the damage done by large investment losses or the true cost of carrying credit-card debt.

Yet I fear compounding isn’t well understood. This has dawned on me over the past month, as I’ve been teaching an undergraduate course on personal finance. Many of my students repeatedly make the mistake of adding together investment returns. For instance, if an investment earns 10% this year and 10% next year, they think the cumulative gain is 20%. But in truth, you would make 21%. The reason: In the second year, you earn 10% not only on your original investment, but also on the money earned during the first year. Thanks to compounding, if you earn 10% a year, you double your money roughly every seven years.

But compounding isn’t always your friend. It also comes into play with debt, as you incur interest not only on the original sum borrowed, but also on interest from earlier periods that wasn’t repaid. This is the trap that many credit-card borrowers fall into, as their minimum payments barely offset the financing charges they incur.

Just as my students add together investment gains, they also make the mistake of adding together gains and losses. For instance, if a hypothetical investor loses 50% this year but makes 50% next year, many of my students think our investor is back to even. But in fact, the cumulative result is a 25% loss. The grim reality: To recoup a 50% loss, you need a 100% gain. This highlights the danger of betting heavily on a few stocks, buying investments with margin debt and purchasing leveraged exchange-traded index funds.

Struggling with the notion of investment compounding? You might try playing around with a simple investment calculator, such as the one offered on Dave Ramsey’s website. Unfortunately, the calculator doesn’t allow you to assume a negative rate of return. But it does show how your money can balloon, given enough time, good savings habits and even a modest rate of return.

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