He'd never even bought a lottery ticket, but one St. Louis man was recently treated to a $1.6 million surprise. The money was his all along -- he'd just forgotten all about it, until Missouri's investigation of forgotten financial accounts reconnected him with his long-lost cash. His lucky day is also a valuable lesson in the power of compounding investments.

You see, his account didn't have $1.6 million in it when it first slipped his mind. It grew to that size over time, invested in stocks or a stock fund. As this chart of compound annual returns between 1926 and 2008 shows, stocks are a powerful wealth-building tool:

Asset Class

Return

Small stocks

11.7%

Large stocks

9.6%

Government bonds

5.7%

Treasury bills

3.7%

Inflation

3.0%

Source: Ibbotson.

Over that lengthy period, a $1,000 investment would have grown to more than $9.5 million in small stocks, $2 million in large stocks -- or less than $100,000 in government bonds.

It's all in the timing
For all we know, the lucky guy in question could have started out with an account worth $3 million, and wound up with his considerably smaller sum because of bad investment choices.

But it's far more likely that his account grew over time. If he started with $100,000 and left the money there for 50 years, it would have averaged 5.7% in returns annually, which isn't all that impressive. If it grew at 10%, it would have needed only 29 years to reach his eventual payday. To hit $1.6 million in only 20 years, the rate would have had to be almost 15%. Playing with numbers and scenarios like this shows how important your growth rate is to your eventual return, and how powerful an ally time can be.

How we can accumulate $1.6 million
That 15% annual gain is far from impossible. The following companies' 20-year stock returns are either close to that figure, or even higher:

Company

20-Year Avg. Annual Return

General Dynamics (NYSE:GD)

27.5%

Schwab (NASDAQ:SCHW)

24.0%

Applied Materials (NASDAQ:AMAT)

18.8%

Adobe (NASDAQ:ADBE)

17.2%

Nike (NYSE:NKE)

18.3%

Walgreen (NYSE:WAG)

15.1%

Texas Instruments (NYSE:TXN)

14.7%

Data: Yahoo! Finance.

With a little work and patience, you could create a windfall of your own, whether you do so via bargain-priced stocks or a simple index fund. If you park $1,000 in an index fund today, you could leave one heck of a surprise for your grandkids in 50 years.

Longtime Fool contributor Selena Maranjian does not own shares of any companies mentioned in this article. General Dynamics is a Motley Fool Inside Value pick. Adobe Systems and Charles Schwab are Motley Fool Stock Advisor selections. Try any of our investing newsletters free for 30 days. The Motley Fool is Fools writing for Fools.