It's natural to dream about being wealthy -- but what does that mean in terms of dollars? You might think $1 million in savings would do the trick, but actually, that's not even close. Americans believe that it takes an average of $2.3 million in personal net worth to be considered wealthy, according to Schwab's 2019 Modern Wealth Survey. That's over 20 times the median net worth of U.S. households, going by Federal Reserve data released in 2017.

Now clearly, $2.3 million is a lot of money to amass. But Americans are surprisingly optimistic about their ability to become wealthy. More than half think they'll achieve that goal in their lifetime, while 40% think they'll get there within a decade. If you'd like to join the ranks of these aspiring wealthy Americans, a few smart financial moves could very well help you get there.

Man counting hundred-dollar bills

IMAGE SOURCE: GETTY IMAGES.

Save early, and save wisely

If your goal is to be wealthy, you really need to do two key things: Start saving money early on in your career, and put that money to work by investing it. The more time you give your money to grow, the more you'll get to benefit from the power of compounding.

Today's tax-advantaged retirement plans make it easy to accumulate wealth, because they allow your money to grow on either a tax-deferred or a tax-free basis. This means that you don't have to pay taxes on your investment gains year after year, and as such, you're free to reinvest them for added growth.

Currently, you can sock away up to $19,000 a year in a 401(k) if you're under 50, or up to $6,000 a year in an IRA. If you're 50 or older, you get a catch-up provision that raises these limits to $25,000 and $7,000, respectively.

That said, maxing out a 401(k) is a pretty challenging thing to do when you're an average earner. The good news? You don't have to max out to eventually amass enough money to be wealthy as per the above definition. You just have to save consistently from a young age and invest your savings the right way.

Check out the following table, which shows what a monthly $500 savings contribution might grow into based on your savings window:

If You Start Saving $500 a Month at Age:

Here's What You'll Have by Age 67 (Assumes an 8% Average Annual Return):

22

$2.3 million

27

$1.5 million

32

$1 million

37

$680,000

42

$439,000

Data source: AUTHOR.

If you only give your savings 25 years to grow (which, in our example, is the case if you first start saving at 42), you don't earn all that much on your money. But check out the first line of the table. Contributing $500 a month to savings over 45 years means putting in $270,000 of your own money. And if you score an 8% average yearly return on your savings, you'll wind up with that coveted $2.3 million. Not only is that a very impressive number, but it also represents more than a $2 million gain on the amount you initially put in.

And that leads to the second half of the winning formula I've outlined -- investing wisely. The 8% return is actually just below the stock market's historical average. If you load up on stocks, which you should feel comfortable doing as long as you have a 10-year investment window or longer, you might easily score an average yearly 8% return or higher.

Best of all, you don't need to be an investing genius to do well with stocks -- you can load up on index funds, which effectively allow you to put your money into a bucket of stocks and benefit from their collective performance. It's often a less stressful way to go than researching specific companies and buying individual stocks -- though if you're willing to put in the effort, that can be a rewarding way to invest, too.

Of course, just because Americans landed on $2.3 million as the definition of wealthy in one survey doesn't mean you should feel bad about yourself if you're sitting on $1.5 million at present. (And, for the record, $2.3 million in personal net worth doesn't necessarily mean $2.3 million in a savings account or retirement plan. It could be a combination of savings, home equity, and other assets.)

There are many ways to define wealth, and one you might care to go with is having enough money to live the way you want to. But if you're eager to hit that $2.3 million mark, know that with the right savings and investing approach, it is possible.