Let's look at some examples, to see how it can work.

Compounding is when something grows over time, and the amount by which it grows is also growing. It's much easier to understand when you consider some examples. (Math alert! Math alert! Keep reading, though -- it's just multiplication, and it's very important stuff.) Let's start with a simple example. We'll use 10% as our annual growth rate and start small, with $100. Let's call this Year 0, when we start with $100. One year later, in Year 1, our $100 has grown by 10%. Since 10% of 100 equals $10, we add that to our money and end the year with $110. Got that? (Note: Remember, to find out what 10% of anything equals, just multiply the number by 0.10. To find 5%, multiply by 0.05. For 25%, by 0.25.)

In Year 2, we add another 10%. But this time you don't end up with $10. Ten percent of $110 is $11. So we end Year 2 with $121 ($110 plus $11 equals $121). In Year 3, we add 10% again, or $12.10. Our new total is $133.10. Here's a table that will make it clearer:

Do you see what's happening? Your initial bundle of $100 is growing, and the amount by which it's growing is also growing. That's compounding in action. In just eight years, you doubled your money. If you had just added 10% of $100 each time, that would have been $10 every year, and you'd have ended up with $180. But since your money was compounding, it grew faster.

If this doesn't seem magical enough for you, here's a continuation of the earlier table, showing certain years that are farther out:

Now that's magical, isn't it? Here are a few key things to notice:

• You started with just one single investment of $100. In Year 25, your wealth grew by $108! In that single year, you made more than your entire initial investment. And the following year, you made even more than that.
• Notice how large the total gets. You started with $100, but in 50 years, that's become almost $12,000. (A stickler might point out that thanks to inflation you won't be able to buy as much stuff in 50 years with that $12,000 as you could buy with $12,000 today. But then, today you just have that $100. You're still coming out way ahead.)
• Notice that the longer you let your money compound, the more massive each year's growth becomes. In the first years, you just added $10 or $20 or $30 per year. But after 25 years, you're adding hundreds each year. Compounding gets more powerful the longer it's left to work.

The Growth Rate

If you're not yet finding this fascinating, then perhaps the next few tables will do it for you. Remember that we used a growth rate of 10% in our example above. The growth rate -- how fast your money grows, on average, from year to year -- is very important. Let's start over, using $100 again, but compounding at three other rates of growth: 5%, 11%, and 15%. Five percent is what you might earn in interest in a bank account in some years, or on a CD (certificate of deposit) or on some bonds. Eleven percent is the historical average growth rate per year of the stock market for most of the last century. Fifteen percent is how fast your money might grow if it were invested in a bunch of top-notch companies that you selected on your own.

If you start with $100, and it grows at 5%, 11%, and 15%, here's how much you'll have after various periods of time. (The pennies have been rounded off to the nearest dollar.)

Pretty impressive, eh? Here are some things you should notice or be aware of:

• Again, see how the amount by which the sum grows is increasing as the years go by. For example, growing at 11%, your total increases by around $200 between years 10 and 15. But in a later five-year period, between years 40 and 45, your total grows by more than $4,000!
• Don't let these long time frames put you off. If you're 15 years old now, you probably can't imagine being 55 or 65. That's reasonable. Soon we'll discuss how you can move things along more quickly. Just let these tables show you how compounding works and how it gets more and more powerful as the years go by.
• Finally, notice what a huge difference the growth rate makes. If your money is growing at 15% instead of 5%, you'll end up with about four times more money after 15 years. Even though 11% and 15% might not seem so far apart, over 20 years, you'll end up with twice as much money. Stretch that out over 50 years, and you'll have nearly six times more money at 15% instead of 11%.
• Notice that, growing at 15% per year, a single $100 investment can turn into more than $100,000 over 50 years.

Interest vs. Stock Market Returns

Keep in mind that not all growth rates are the same. If your bank is paying 3% interest on your savings, that's pretty much guaranteed money. If a savings bond is paying you 5% interest, that's also darn close to a sure thing. (Interest rates change over time, though, so your bank might be paying you 1% in some years and 6% in others.)

The stock market, however, is not a sure thing, and neither are some bonds issued by companies. Stock market returns fluctuate. There are good years, great years, so-so years, and years we'd much rather forget. Over long periods of time, though, the stock market tends to go up. Over many decades, it has averaged an annual 11% return.

Similarly, with companies, many remain strong for decades or a century. Others fail. If you select and invest in solid, growing companies, you can hope to earn as much as 15%, on average, per year. If you select one or more companies that turn out to be remarkable growers, such as Microsoft, the average growth rate for your investments might be higher than 15%.

In general, the more certain the growth rate, the lower it will be. The more iffy it is, the higher it will be. We'll cover these topics in more detail later. For now, just understand that most growth rates are not sure things. (That's okay, though. You can still make a lot of money by investing.)

The Amount of Money You Invest

You should now have a sense of how money can grow over time, and how much growth rates matter. Now let's turbocharge our results by upping how much money we start with. Instead of starting with an initial investment of just $100, let's see what happens with $1,000.

By the way, if $1,000 seems like an awful lot to you, realize that it's really only $20 per week. Accumulating $20 per week to save isn't as difficult as you may think. In another article we offer you a bunch of good ideas.

If you start with $1000, and it grows at 5%, 11%, and 15%, here's how much you'll have after various periods of time:

Lookie there -- in 50 years, $1,000 becomes $1 million! (If only your grandparents had invested $1,000 for you 50 years ago, eh?) The point of this table is just to show you: the more you invest, the more money you're likely to end up with.

Is Your Head Hurting?

Is all this math stressing you out? We're almost done. This is extremely important stuff -- stuff that could change your life. Don't think of it as just math -- think about what the tables represent. They show you how small sums of your money can grow into large sums. You can start with enough money to buy a CD player, and end up with enough to buy a car or a house or a trip around the world.

Many adults find that these tables make their heads hurt, too, but for a different reason. It's because when they realize what these tables are saying, they start banging their heads against a wall, wishing they'd known about this stuff when they were younger.

Investing Money Regularly

Let's tweak these tables one last way, to make them more realistic. After all, how likely is it that you'd invest just $100 or $1,000 in one shot at your age, then add nothing else for the rest of your life? Here's what happens when you invest money regularly.

Investing $100 Each Year