Soon, you'll be seeing a bit more money in your wallet, thanks to the government's latest stimulus package. If you play your cards right and don't just go blow it on an extra lunch or a trip to the movies, you could make yourself a millionaire over time.

Watch or you might miss it
Even though workers are slated to start receiving stimulus money as early as later this month, you might not even notice the stimulus when you start getting it. Rather than a big check for $600, $1,200, or more like you got in 2008, the government isn't making lump-sum stimulus payments this time around. Instead, you'll see a small reduction in the taxes withheld from your paycheck -- an average of $10 to $15 per week for single taxpayers, and around $15 to $20 for couples.

Now you might think that even at the upper end of that range, $20 isn't going to go too far. But given enough time, you can turn that $20 into a whole lot more -- and learn a lot about investing in the process.

Where to find explosive returns
Now don't get me wrong: It won't be an easy trip. At first glance, you might think the math would make it impossible: $1 million divided by $20 per week equals 50,000 weeks, or just a few decades shy of 1,000 years.

But that's where the magic of compound returns again rears its head. Find an investment with good enough returns, and you'll be on the path to millionaire status long before people start partying like it's 2999.

Still, even with compounding helping you, you've got a tough task. Depending on how much time you have to invest, here's the returns you'd need to earn on average to reach the million-dollar mark from a weekly $20 investment:

Time to Invest

Average Annual Return Needed

20 years

28%

25 years

21%

30 years

17%

35 years

14%

40 years

12%

That's a tall order in any market; especially after the losses you've seen lately, you might think it's well-nigh impossible to reach your goals.

Enter small-cap stocks
Sure, it's a bit crazy to think that you could turn $20 a week into $1 million with anything less than perfect investments. If you stick with well-established S&P 500 large-cap stocks with market caps of $25 billion or more, you'll need some luck:

Stock

10-Year Average Return

Gilead Sciences (NASDAQ:GILD)

32.3%

Apple

27.8%

Occidental Petroleum (NYSE:OXY)

23.3%

Qualcomm (NASDAQ:QCOM)

17.1%

Altria (NYSE:MO)

13.0%

Source: Capital IQ, a division of Standard and Poor's; returns for 10 years ended March 31, 2009.

As you can see, a few stocks have produced great returns in the last decade. But nearly half those $25 billion-plus companies have actually lost money since 1999.

But there's a much more promising area to find stocks that could potentially produce the 12%, 14%, or even 17% long-term returns that you'd need to create a million from a 20-spot. You'll find those opportunities among small companies. Consider:

  • Small caps have room to grow and outperform their larger competitors.
  • Small caps don't have a Wall Street following that tends to inflate prices.
  • Small caps can act quickly to take advantage of changing economic conditions.

Even just looking at the smaller companies in the S&P 500 -- companies that until recently were small caps -- tells you just how much more potential these stocks have:

Stock

10-Year Average Return

Southwestern Energy (NYSE:SWN)

43.2%

Celgene (NASDAQ:CELG)

42.3%

XTO Energy (NYSE:XTO)

40.4%

Range Resources

35.1%

Cognizant Technology

34.7%

Make a million
Of course, there's no guarantee that even small-cap stocks will produce high enough returns to turn $20 into $1 million over time. You'd certainly need a much better market than you've seen in recent months.

But with a healthy number of strong small caps holding up even in this bear market, they're definitely worth using to take a fair shot at becoming a millionaire. Even if you fall short, you'll almost certainly end up with a lot more than $20.

For more on investing in small caps, read about:

To get more small-cap investing ideas, check out our Motley Fool Hidden Gems newsletter -- it's completely free with a 30-day trial.

Frustrated with your 401(k)? Even if your employer's plan isn't the greatest, you don't have to give up your dreams of a happy retirement. Get the tips you need to turn your retirement savings around in our special report, "How To Make The Most of Your 401(k)" -- just click here for instant free access.

Fool contributor Dan Caplinger hopes to turn that $20 a week into something more than just another night out. He owns shares of Altria. Apple is a Motley Fool Stock Advisor recommendation. Try any of our Foolish newsletters today, free for 30 days. The Fool's disclosure policy treats you like a millionaire.