Naturally, any of us would love to double our money -- and then, perhaps, double it again and again. Clearly, this can be done, and many people have done it, but you might be assuming that you're not the kind of person who can.

Nonsense. You don't need to be a savvy stock market operator in order to harness the market's power to make you richer. Here's how you can go about doubling your money.

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The Rule of 72

It all boils down to math: Doubling your money is a function of how rapidly your money grows in value, and the time in which it grows. The Rule of 72 can help you see how money doubles: Per the rule, if you divide 72 by your growth rate, you'll get the number of years it will take to double your money. You can also divide 72 by the number of years in order to get the annual growth rate needed to double your money. Check it out:

Growth Rate

Years to Double

2%

36.0

3%

24.0

5%

14.4

7%

10.3

10%

7.2

12%

6.0

15%

4.8

20%

3.6

25%

2.9

Source: Author calculations.

Years to Double

Growth Rate

3

24%

4

18%

5

14.4%

6

12%

7

10.3%

8

9%

9

8%

10

7.2%

15

4.8%

20

3.6%

Source: Author calculations.

According to the tables, a $100 investment growing for six years at 12% will become $197. The rule is surprisingly accurate much of the time, but it gets less so as the growth rates get very steep. A $100 investment growing at 24% for three years, for example, will grow to $191, not $200. Still, it's in the ballpark.

How to double your money

So clearly, all you need to double your money is time -- or hefty growth rates, if you're in a hurry. No one should be expecting average annual gains in the high teens or above, though it can happen. But the long-term average annual return of the stock market is close to 10%, and it could be significantly higher or lower over the 20, 30, or 40 years in which you invest.

Here are some ways to get good returns on your money in stocks:

Index funds

Index funds are passively managed mutual funds, meaning that they simply own whatever holdings are in the index that they track. Many index funds track the S&P 500 index of 500 of America's biggest companies, which together make up around 80% of the overall U.S. stock market's value.

It's hard to beat index funds, because many of them charge minuscule fees and deliver roughly market-matching returns -- while outperforming most mutual funds actively managed by well-paid financial professionals.

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Dividend payers

Index funds require very little work on your part and are really sufficient for most of us. But if you have the time and interest, you can learn much more about investing and start adding some carefully chosen individual stocks to your mix as you aim for market-beating returns.

A great place to start is with dividend-paying stocks. Not only do they pay a fairly dependable dividend regularly (which you can use to invest in additional shares of stock), but those dividend payments tend to increase over time. And on top of that, the stock's own value is likely to increase over time, too, assuming it's tied to a healthy company.

Imagine that you've got a growing nest egg worth around $300,000 right now, and it has an overall average dividend yield of 4%. That would generate around $12,000 per year, or about $1,000 per month -- meaningful income that would be very helpful in retirement, or that could buy a lot more stock.

Growth stocks

Growth stocks are another kind of stock to consider adding to your portfolio. They're tied to companies that are growing relatively briskly, and they often trade at premium prices because investors have bid their prices up due to high expectations. When those expectations are met -- or exceeded -- the growth investor does well. (And often, very well.) But not all growth stocks will perform as expected, and sometimes overvalued stocks will simply drop closer to their intrinsic value. So you need to pay attention to valuation and expect volatility.

A good way to be a growth stock investor, per our Motley Fool Investing Philosophy, is to buy 25 or more stocks, expecting to hold them for at least five years. That gives you a decent chance of ending up owning at least one or more huge winners, and it also gives the companies time to grow and the stocks time to perform.

Those are three approaches to doubling your money in the stock market. You can mix and match, perhaps doing a bit of all three, or you might very reasonably just stick with index funds. If they deliver average annual growth of 10%, you might double your money in 7.2 years.