How Money Compounds

SUPPOSE YOU EARN 10% this year and 10% next year. Your cumulative gain would be 21%. Why? Imagine you invested $100. The first year’s 10% gain would turn your $100 into $110. Because you start the second year with $110, the next year’s 10% gain boosts your portfolio’s value by $11, not $10. That brings your total to $121, for a two-year cumulative gain of 21%.

Got a series of annual returns for which you’d like to find out the cumulative gain? Divide each return by 100 and add 1, and then multiply the numbers together. For instance, a 10% return would become 1.1. Again, let’s assume you earned 10% in two consecutive years. Here’s the calculation:

1.1 x 1.1 = 1.21

To turn the 1.21 back into a percentage, you would reverse the earlier calculation, first subtracting 1 and then multiplying by 100, which in this case would give you 21%.

What if you lost money during one year and you want to calculate your cumulative return? Once again, divide by 100 and add 1. In the case of a negative return, it becomes something less than 1—but it will always be a positive number. For instance, if you lost 10% in a year, that loss would be represented by 0.9. Here’s how the math would look if you lost 10% in the first year and then gained 10% the following year:

0.9 x 1.1 = 0.99

To turn this back into a percentage, you would follow the usual procedure—subtract 1 and then multiply by 100—which would give you a cumulative return over the two years of -1%.

Seems complicated? For an explanation that doesn’t dwell too much on the math, check out this video from Money magazine.

Next: Annualized vs. Cumulative Returns

Previous: Investment Math

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