The stock market turns ordinary people into millionaires every day, and it's actually one of the easiest ways for the average person to grow wealth. The sheer number of investment options can be intimidating and the risk of loss concerning, but overcoming those obstacles is actually a lot easier than you think.

Here's a look at one of the simplest ways you can turn $10,000 into more than $450,000 using the stock market.

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How does the stock market grow your money?

When you invest in a stock, you buy an ownership stake in the company at whatever the current market value is. You can hold on to that for as long as you'd like. Then, when you need money, you can sell it at whatever the current market value is. The difference between what you initially paid for the stock and what you sell it for is known as your earnings.

If you've invested wisely, the market value of your shares should go up over time. Stock prices can change wildly in the short term, sometimes rising and falling many times within a single day. But over the long term, the S&P 500, one of the best-known market indexes, averages about a 10% return per year.

That means that if you invested in an index fund containing all the same stocks as the S&P 500, you could also see your savings grow by an average of about 10% per year over several decades. Your actual return will likely be a little less than that of the index itself because index funds charge annual fees to shareholders. However, these fees are usually pretty low, amounting to a few dollars per year for most people.

How to turn $10,000 into over $450,000

If you invested $10,000 into an S&P 500 index fund today and it had a 10% average annual rate of return over the next 40 years, you'd end up with nearly $452,600. And that's without ever investing another dime after the initial $10,000.

Those who routinely invest more money could end up with a much larger sum, as could those who reinvest their dividends, excess earnings that companies split with their shareholders. Not all stocks pay them, and those that do usually only pay them quarterly. They're often only a few dollars, but they can still add up over time, especially after being reinvested for a few decades.

Now, I imagine some of you are thinking, "That's great for someone who has $10,000 to spare, but I don't." And the good news is you don't have to. You can reach the same $450,000 over 40 years by investing less than $81 per month, assuming you still earn a 10% average annual rate of return.

You'll contribute more of your own money this way. Investing $81 per month for 40 years will cost you close to $39,000. That's because a lot of your funds won't be invested for the full 40 years. But it's a lot easier for most people to set aside a few dollars every month than to come up with thousands of dollars all at once.

The beauty of investing this way is its simplicity. All you have to do is keep putting in money, and the index fund will do the rest of the work for you. It'll automatically give you an ownership stake in hundreds of companies across several industries, so your savings are diversified. This helps reduce your risk of substantial loss. 

The only other thing you really need is patience. You will likely experience some ups and downs along the way, but as long as you trust your investment strategy and avoid emotional decisions, you can grow yourself a pretty substantial nest egg over time.