As the old saying goes, your first million is the hardest. Once you've got a decent chunk of money, compounding does much of the hard work to help your nest egg grow. That's what makes a $100,000 account value a great milestone along your journey to wealth. It's large enough that compounding can actually add significant amounts to your balance, while being small enough to potentially reach it fairly early in your career.

With that in mind, these four ways to grow $100,000 into $1 million for your retirement savings can help you get through that time period where compounding really starts to do the hard work on your behalf. With one or more of them at your disposal, you can give yourself a better shot of reaching millionaire status by the time you're ready to retire.

Investor pointing to an upward growth chart.

Image source: Getty Images.

No. 1: Reinvest your dividends somewhere

Historically, dividends have provided somewhere in the neighborhood of a third of total market returns. In a time of heightened volatility where the market can surge or plunge seemingly overnight, the relative stability of dividend payments can play a stronger role than they could in a raging bull market.

After all, dividends are typically paid out of a company's operating earnings, and those earnings don't depend on the market's current sentiment. When that cash shows up while stock prices are low, the same number of dollars can buy that many more shares. Although any given dividend may seem small, and the temptation may be to spend it, put them all together, and they can add up to a decent chunk of your total returns.

No matter how much you get from dividends, reinvesting them somewhere -- even if not in the company that paid them -- can be an important source of the compounding that builds your wealth.

No. 2: Put your money in index funds

Over long period of times, investing in index funds tends to beat owning actively managed mutual funds. This is largely because actively managed funds need to cover higher internal management costs than index funds do. The funds themselves provide the source of that money, so active funds need to beat passive ones by more than the cost of their fees in order to outperform them overall. That's a high hurdle to clear, hence why actively managed funds tend to underperform the general market.

That does raise a potential issue, though. The stock market has delivered average annualized returns somewhere in the neighborhood of 9% to 10% over long periods of time, and those returns are never guaranteed. At 10% annualized, it would take just over 24 years for $100,000 to turn into a $1 million nest egg. At lower returns, it would take even longer. While that's feasible if you're able to keep working for that long, it gets a little rough if you don't quite have that much time left before you retire.

No. 3: Keep adding to your nest egg along the way

Of course, there's no rule limiting your ability to save new money just because you've reached that $100,000 milestone. Continuing to add new money as you're able to do so gives you a tremendous boost on that journey to $1,000,000. Socking away just $100 a month could knock two years off that time, taking the total to just above 22 years. Make it $1,000 per month, and you could see your initial $100,000 nest egg grow to where you reach millionaire status in just over 16 years.

A potentially great way to add that money is to contribute to your Roth 401(k) or similar plan at work if one is offered to you. With such a plan, you add after-tax money to your retirement account straight from your paycheck. It then grows tax-deferred throughout your career, and then you can typically take tax-free withdrawals from such an account once you retire.

If you're under age 50, you can generally contribute as much as $20,500 per year to your Roth 401(k). If you're 50 or older, you can add an additional $6,500 to your limit, for as much as a $27,000 total. That makes the standard monthly contribution limits just over $1,700 for folks under 50 or $2,250 for those age 50 and up. That can be a great accelerator to your wealth-building plans, and you can make it happen starting with a simple payroll or HR form at work.

No. 4: Try to invest to beat the market

Just because it's hard for professional investors to beat the market after accounting for their fees doesn't mean it's impossible for individuals to do so. There are a number of paths that have historically offered opportunities for regular people to beat the market. Warren Buffett, for instance, made his fortune as a value investor, focusing on finding companies that traded at or below a reasonable estimate of their intrinsic net worth.

His approach is a bit harder to accomplish today, now that faster information flow and electronic access to the markets mean that values don't tend to stick around as they used to. Still, the framework of understanding what a company is really worth and making a commitment to not overpaying for that worth can still serve investors well today.

An alternative approach to try to beat the market is to focus on smaller companies. Smaller companies may be earlier in their growth curves, and thus, have the opportunity to increase in value by a greater percentage than the market's current behemoths. In addition, Wall Street tends to focus less on smaller businesses, making it more likely that good ones might slip through the cracks for you to find before they do.

Even there, though, there are trade-offs. After all, small companies tend to have fewer financial resources than larger ones do. That may make them more vulnerable to tough economic times or the downsides of choices that don't quite go the way they hoped.

The advantage of following a path that might beat the market is that if you succeed, you can reach that $1 million mark faster. The disadvantage is that there are certainly no guarantees that you'll be able to do so.

No matter what approach you take, it makes sense to start today

Regardless of path you take to attempt to grow your $100,000 nest egg into $1 million, the reality is that it will very likely take you at least a decade to reach that target -- quite possibly two or more decades. As a result, the sooner you get started, the sooner you have a chance of actually reaching your goal. So get started today, and give yourself the longest possible runway to reaching retirement as a millionaire.