Without independent savings, you risk struggling to pay the bills during retirement. That's why it's important to contribute money to your nest egg throughout your working years. But the type of account in which you house your money could dictate how much growth you see on your savings, and in this regard, a large number of Americans are making a massive mistake.

An estimated 46% of U.S. workers use a regular savings account to sock away funds for retirement, according to GOBankingRates. Meanwhile, 30% are saving for their golden years in a 401(k), while 14% are putting their money into an IRA.

The problem with housing that money in a savings account, though, boils down to the fact that you can't invest it. As such, you're limited to whatever interest rate that account is paying, which is apt to be far below what you'd get with a diversified investment portfolio, which 401(k)s and IRAs allow for. And that could be disastrous for your retirement.

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You need aggressive growth

One benefit of keeping money in a savings account is that your principal is protected from losses, up to $250,000 per depositor. When you invest money in an IRA or 401(k), you do run the risk of taking losses when the market declines or downright tanks, as it tends to do from time to time. But if you keep your money invested for a lengthy period of time, you're far more likely than not to come out ahead, especially if you do a good job of diversifying. And if you limit yourself to a savings account, your nest egg won't grow in a manner that allows you to keep up with inflation.

Imagine you're able to set aside $300 a month for retirement. The following table highlights the difference between housing that cash in a savings account versus an IRA or 401(k).

Savings Window (Assumes a $300 Monthly Contribution)

Ending Savings Account Balance (Assumes a 1% Average Annual Return)

Ending IRA/401(k) Balance (Assumes a 7% Average Annual Return)

20 years

$79,269

$147,587

25 years

$101,677

$227,702

30 years

$125,227

$340,066

35 years

$149,978

$497,663

40 years

$175,992

$718,701

CALCULATIONS BY AUTHOR.

Look at that last row. The same $300 a month over 40 years could leave you with just under $176,000, or with close to $719,000. That's a world of a difference. But an average annual 1% return is what you're likely to snag in a savings account based on today's rates, whereas the 7% return used above is actually a few percentage points below the stock market's average, which means that if you go heavy on stocks, which you should over a 20- to 40-year investment window, you're likely do that well, if not better.

Think about the tax savings, too

Not only do IRAs and 401(k)s offer more opportunity to grow your money, but they also let you capitalize on tax incentives in the process. With a traditional IRA or 401(k), your contributions are made on a pre-tax basis, which means that if you're putting $300 a month into either account, that's $300 in earnings the IRS can't tax you on. Also, investment gains in a traditional IRA or 401(k) are tax-deferred, which means you won't pay them year after year; you'll just pay taxes on your withdrawals during retirement.

Roth IRAs and 401(k)s work the opposite way: You don't get an immediate tax break on the money you contribute. But once that cash is invested, it gets to grow completely tax-free, and withdrawals in retirement are taken tax-free as well.

With a savings account, however, you don't get any tax breaks -- contributions are always post-tax, and interest income is taxable on a yearly basis. Of course, you do get the option to withdraw your money from a savings account at any time, whereas with an IRA or 401(k), you'll be penalized if you remove funds before age 59 1/2. But when you're saving for retirement, you actually don't want that option, because the more you take advantage of it, the less money you'll have available when your golden years roll around.

Though a savings account is a great place to house your emergency fund, it's the wrong place for your nest egg. Read up on how IRAs and 401(k)s work, and choose one of these plans to accumulate wealth for retirement instead.

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