Here’s how much you need to save each month to be a millionaire in 15 years

Editor's note: Calculations in this story have been revised by using a more accurate tool.

Young people are pretty confident about their financial futures. A recent survey from TD Ameritrade found that 53 percent of millennials expect to become millionaires at some point in their lives, if they aren't already.

While 23 percent believe they'll hit $1 million by age 50 or older, many expect to get there more quickly. A full 19 percent say they'll become a millionaire by age 40 and 7 percent predict it'll happen by 30.

But what if you want to speed up the process and reach that milestone in the next 15 years? It could be possible, if you're willing to work for it — and put away much more each month than the average American.

Using Bankrate's millionaire calculator, CNBC Make It found how much you'd have to save each month to become a millionaire by 2033. Here's how much you'll need to put away, depending on the amount you already have invested.

With a 4 percent rate of return: $4,075 per month
With a 6 percent rate of return: $3,500 per month
With an 8 percent rate of return: $2,945 per month

With a 4 percent rate of return: $4,000 per month
With a 6 percent rate of return: $3,375 per month
With an 8 percent rate of return: $2,850 per month

With a 4 percent rate of return: $3,930 per month
With a 6 percent rate of return: $3,325 per month
With an 8 percent rate of return: $2,775 per month

The average annualized total return for the S&P 500 index is more than 9 percent. But it's important to keep in mind that these calculations don't account for the many variables that can affect wealth over several decades, including windfalls, emergencies and rises or dips in the market.

Of course, saving hundreds or thousands a month is an ambitious goal. Even $1,000 a month is more than most Americans can manage. But getting into the habit of saving any amount will be great for you in the long run.

Here are a few simple, low-stress ways to start investing:

• Sign up for your employer's 401(k) plan and take full advantage of any company match, which essentially gives you free money
• Contribute to a Roth IRA or traditional IRA, an individual retirement account that offers tax breaks
• Use micro-investing apps such as Acorns, which help you begin by investing small amounts of what it calls your "spare change." The app rounds up your purchases to the nearest dollar and automatically puts your coins to work
• Try other apps that aim to make investing simple
• Consider automated investing services known as robo-advisors that can help you out no matter how much you have in the bank
• Research low-cost index funds, which Warren Buffett recommends

Correction: This story has been revised to use a more accurate calculator tool.

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