Saving independently for retirement is imperative because without personal savings, you might struggle to pay your bills later in life. This might especially hold true if Social Security cuts come down the pike, which is a possibility based on the program's financial situation.

If you have access to a 401(k) plan through your employer, you may be inclined to make the most of it. And you might assume that the best approach to your 401(k) plan is to try to max out by contributing as much as you can. But actually, there may be a better approach to funding your 401(k).

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Maxing out isn't automatically your best bet

Although maxing out a 401(k) isn't easy, it's something you may be pushing yourself to try to do. But actually, there's a very good reason not to max out a 401(k) plan.

See, 401(k)s are notorious for charging high administrative fees. So the more money you put into one of these plans, the more you might lose in the form of fees.

Also, 401(k) plans tend to limit your investment choices. You can't buy individual stocks in a 401(k), generally speaking, so you're usually looking at a few dozen funds to choose from.

Some of those funds -- notably, mutual funds and target-date funds -- may come with notably high fees. Those could eat away at your returns over time, the same way administrative fees can.

Rather than aim to max out your 401(k) plan, a better strategy may be to put in just enough money to claim your employer match in full. But from there, you may want to put the rest of your savings elsewhere.

An IRA could make more sense

One benefit of IRAs over 401(k) plans is that they generally do make it possible to handpick stocks for your retirement portfolio. And that's an option that could work to your benefit over time.

Let's say you contribute $300 a month to your 401(k) over a 30-year window and invest that money in the S&P 500 index funds your plan makes available. The S&P 500's average return over the past 50 years has been 10%, so let's say that's the return your 401(k) generates, as well. In that case, you'll be sitting on about $592,000 at the end of your savings window, which isn't too shabby.

Meanwhile, let's imagine that your $300 a month is going into an IRA, instead, and you create a stock portfolio based on thorough research. If your picks deliver an average annual 12% return instead of 10%, you'd end up with more like $869,000 in retirement savings. That's a big difference.

Of course, none of this accounts for fees. And to be fair, these numbers don't account for an employer match, either.

The point, however, is to illustrate that a 401(k) plan may not be your best retirement savings choice due to the fees you might pay and the extent to which your investing strategy may be thwarted. While it definitely pays to fund your 401(k) plan to snag your full employer match, you may want to limit your contributions to reaching that goal. Once you achieve it, you can save in an IRA beyond that point.