Young Fools
How to Grow a Million Dollars

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The Magic Word is "Compounding"

The world is full of empty promises. Advertisements tell us to buy this amazing cream because it will make us beautiful or to buy that weird-looking contraption because it will tone our muscles and make us popular.

And here comes the Fool, with another promise. Invest money now and we'll help make you a millionaire, or at least comfortable in your later years. Gee, that sounds even less believable than the beauty cream, doesn't it? But it's true. You can print this out and take it to your math teacher, and he or she can verify it.

If you leave your money to grow for a long time, \$100 can turn into a million dollars. We showed you that in our "Why Invest?" article. But now we want to explain the how and the why a little more. You need to understand what's going on so that you'll believe it.

How does the money grow? By an amazing process called "compounding."

Banks compound money all the time, when they add interest to what is in your savings account. Let's say that you have \$1000 in your account and you're earning 5% on it each year. That means that in one year, the bank will have added 5%, or \$50, to your money. So in year two, you'll have \$1050. In the next year, you earn another 5% -- but now it's 5% of \$1050, not of \$1000. So instead of getting \$50 added to your money, you get \$52.50. At the end of year three, you'll have \$1,102.50. The next year, \$55.13 is added. The year after, \$57.88.

If there was no compounding, you'd get the same \$50 added each year. But with compounding, your money is growing faster and faster. Look at the chart below and you'll see how much is added each year for 25 years.

```Year #  Start with:   Add 5%:
1          \$1,000.00        \$50.00
2          \$1,050.00        \$52.50
3          \$1,102.50        \$55.13
4          \$1,157.63        \$57.88
5          \$1,215.51        \$60.78
6          \$1,276.28        \$63.81
7          \$1,340.10        \$67.00
8          \$1,407.10        \$70.36
9          \$1,477.46        \$73.87
10         \$1,551.33        \$77.57
11         \$1,628.89        \$81.44
12         \$1,710.34        \$85.52
13         \$1,795.86        \$89.79
14         \$1,885.65        \$94.28
15         \$1,979.93        \$99.00
16         \$2,078.93       \$103.95
17         \$2,182.87       \$109.14
18         \$2,292.02       \$114.60
19         \$2,406.62       \$120.33
20         \$2,526.95       \$126.35
21         \$2,653.30       \$132.66
22         \$2,785.96       \$139.30
23         \$2,925.26       \$146.26
24         \$3,071.52       \$153.58
25         \$3,225.10       \$161.25```
See how you begin by just getting \$50 added and end up getting \$161 added? That's compounding. Not only is your money growing, but the amount by which it's growing is also growing.

Here's the simple math. Take 1000. To get 5%, you multiply it by 0.05. The result is 50.

`            1000 x 0.05 = 50.`
Add the 50 to the 1000 and you'll get 1050.
`            1000 + 50 = 1050.`
That's it! Simple multiplication and addition. You can use a calculator or your brain and a pencil. Let's do one more round.
```            1050 x 0.05 = 52.50.

1050 + 52.50 = 1102.50.```

Remember that this is only growing at 5% per year. If you invest your money Foolishly, as we'll teach you to do, you can earn a lot more than 5% a year. And if you want to become a millionaire while you're not too old, you'll probably need to earn more than 5%.

Let's say that at age 18, you decide you can save and invest \$500 per year. How long will it take you to become a millionaire?

Well, it all depends on what you do with the money. If you stuff it into your mattress, you'll be 2,018 years old when it becomes a million intergalactic globodollars. (Unfortunately, you might not be around to enjoy it.) If you park it at a bank, earning 4% per annum, you'll be a 130-year-old millionaire. If you match the average stock market return of 10.5%, you'll get there by age 94. (That's still not too exciting, right? Keep reading.)

Keep in mind, though, that you should be able to beat the stock market and become a millionaire a lot sooner. If you take the time to learn a lot and become an excellent investor, earning perhaps 16% or more, on average, per year, you could be a millionaire in your 60s. And this assumes you won't save more than \$500 a year -- which you will, right? By investing intelligently, you can get to a million in a few decades -- starting with just a few hundred bucks.

Try experimenting with compounding. You can do it the old fashioned way, with paper and pencil, or the less old-fashioned way, with a calculator. Or fire up our friend the web and use The Motley Fool's snazzy Fool Compoundulator. You just plug in how much you're starting with, how much and how often you'll invest more, how long your money will grow, and by what percent your money will grow. Then tell it to "Compoundulate" and you'll see how much money you'll end up with. Try changing the numbers you enter and see what happens.