Many people have the goal of retiring with $1 million or more. And to be clear, that goal may be more than attainable regardless of the retirement plan you save in. But if you have a 401(k), you have a solid opportunity to meet that objective, even if it's the only savings plan you have access to. The key, however, is to manage that 401(k) wisely.

Making the most of your 401(k)

The great thing about 401(k)s is that they come with generous annual contribution limits -- much higher limits than what IRAs allow for. Currently, you can contribute up to $19,500 a year in a 401(k) if you're under 50, or up to $26,000 if you're 50 years of age or older.

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But that's not the only way to pump money into your 401(k). Many employers that sponsor 401(k)s also match worker contributions to different degrees. If you're able to snag a generous match, you could get thousands of free dollars in your account ever year. And best of all, your employer match won't count toward the aforementioned contribution limits.

Now, say you manage to max out a 401(k) at today's levels over 40 years. We'll assume that your savings window spans ages 25 to 65. That alone will leave you with $877,500 if you don't invest your savings at all and therefore see zero growth.

But that's not how 401(k)s are supposed to work. Rather, your goal should be to invest your 401(k) as aggressively as possible to grow your contributions into a larger sum.

If you go heavy on stocks in your 401(k), you might easily enjoy an average annual 7% return on investment, as that's a few percentage points below the stock market's average. If you max out a 401(k) as per the above example, and you enjoy that 7% average yearly return, you'll end up with just over $4 million.

And so there you have it. You can, indeed, retire a millionaire with a 401(k) alone.

But it's not so simple.

Most people don't, in fact, max out their 401(k)s year after year. And many people don't start saving for retirement in their mid-20s, nor do they invest their savings aggressively enough to enjoy the returns we just used in our example.

However, if your goal is to retire a millionaire, don't be like those people. Start setting money aside in your 401(k) as soon as you begin collecting a paycheck. And then make an effort to invest in stocks for generous returns.

This doesn't mean you'll be able to max out your 401(k) every year. But if you set a goal of increasing your savings rate year after year, then over time, you could grow quite a lot of wealth.

Should you save in other accounts if they're available to you?

You may be able to retire a millionaire with a 401(k) alone. But does that mean you shouldn't save your money elsewhere?

If you're eligible for a health savings account, it pays to fund one. The money you don't use for immediate healthcare expenses can be invested for added growth and carried into retirement. And since HSAs offer even more tax benefits than 401(k)s, it's worth participating if you can.

Furthermore, it may not hurt to put some money into an IRA, even if a 401(k) is available to you. IRAs tend to offer a wider range of investment choices, so it could work to your benefit to open one.

That said, before you fund an IRA, make sure to contribute enough to your 401(k) to claim your company match in full. Giving up free money is a poor choice if you're hoping to retire a millionaire.

Commit to that goal

Retiring a millionaire with a 401(k) is more than possible -- if you play your cards right. You may decide to stick solely with a 401(k) for savings purposes, and that's fine. Just be sure to invest wisely and give yourself plenty of years to save along the way.