According to an apocryphal story, physicist Albert Einstein, when asked what was the most powerful force in nature, answered “Compound interest.”

Whether it’s the most powerful force, it is powerful.

Here’s a paragraph from Sterling Futures, October 15, 2021:

Including dividends, the S&P 500 Total Return index, in the five years ended September 30, 2021, gained an astonishing +118%, an average annual growth rate of nearly 24%! That’s more than double the stock market’s long-term annual total return of approximately +10% going back 200 years, as described by Wharton Business School’s professor Jeremy Siegel in his seminal book, Stocks for the Long Run!

Can you spot the error? The authors remembered to take account of compounding when discussing Jeremy Siegel’s book, but forgot to take account of it when computing the average annual growth rate of the S&P 500 Total Return index. They appeared to have divided 118% by 5 to get almost 24% annually.

But here’s the right way. Let x = the annual growth rate. Then (100 + x)^5 = 100 + 118 = 218.

Solve for x, which you can do on an iPhone.

x = just over 16%, which is really good, but it’s not 24%.

The power of compounding.

By the way, Jeremy wrote the entry on stock market returns in David R. Henderson, ed., The Concise Encyclopedia of Economics.