Where you put your savings in your 20s could make a difference of $3 million by retirement

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The reward outweighs the risk.

If you want to finish rich, there's a crucial piece of advice you'd be foolish to ignore: invest in the stock market.

Sure, it's impossible to guarantee big returns or time the market - not even Warren Buffett can do that.

But if you're part of the 46% of millennials staying out of the stock market because it's "too risky," you could be leaving millions of dollars on the table.

That's according to a recent NerdWallet analysis that looked at three potential outcomes for a 25-year-old earning a starting salary of $40,456 (adjusted annually for inflation) and saving 15% each year.

Based on average market returns and interest rates from the last 40 years, NerdWallet calculated that investing in stocks (including in retirement accounts) would lead to $4.57 million by age 65. That's accounting for annual investment fees of 0.70%, but not adjusted for inflation.

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Keeping the money in a traditional savings account - which 63% of millennials are doing today, according to a NerdWallet survey - would result in $1.27 million by retirement, before adjusting for inflation.

The potential opportunity cost to staying out of the market over four decades? $3.3 million.

What's worse, keeping the money out of a bank all together amounts to just $563,436 accumulated over the same time period - an opportunity cost of $4 million.

While NerdWallet's estimation assumes a savings rate of 15%, more than double the current average savings rate in the US, the theory still holds true: When you invest in your 20s, no matter the amount, you're taking advantage of compound interest. You'll have more time to earn money on your savings, and your investments can bounce back from downturns in the market.

"The key here is to get into the market in a way you feel comfortable," says O'Shea. "Then select a few investments that you can dollar-cost average into every month, with repeated and regular contributions. Low-cost index and exchange-traded funds are great options if you want to be more hands on; target-date funds and robo-advisors might be a better fit if you'd like someone or something else to do the work."

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To find out how much money you need to save to finance your retirement lifestyle, start by determining your desired annual retirement income and dividing it by 4% (the maximum amount you will withdraw from your savings each year to pay for your living expenses in retirement). The result is your magic number, or retirement savings goal, and you can leave work as soon as you reach it.

If you expect to live on $50,000 a year in retirement, you'd need to save $1.25 million - an amount you may be able to reach by age 65 if, beginning at age 25, you consistently stash 15% a year in the bank.

But if you're aiming to live on a more generous $100,000 a year, the required savings balloons to $2.5 million. To meet that goal, you'd either need to significantly increase your savings rate, or invest in the stock market for higher returns.

Given the potential opportunity cost associated with not investing, as well as the benefits of compound interest over four decades, investing makes sense. But NerdWallet notes that past market performance doesn't guarantee you'll earn the average historical return of 10% in the future.

Still, a further analysis by NerdWallet found that stock market investors had over a 99% chance of maintaining at least their initial investment - the same as a traditional savings account. But, investors also had a 95% chance of earning nearly three times their initial investment, while traditional savers had less than a 3% chance.

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As it turns out, millennials may finally be discovering that the reward outweighs the risk. According to a recent Legg Mason survey, 78% say they soon plan to invest in the stock market.

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