Social Security only pays the average recipient today about $1,559 a month, so you'll need income on top of that if you want to enjoy your retirement and manage to cover your bills with ease. That's where your savings come in.

Now the reality is that some people can get by nicely in retirement with several hundred thousand dollars in savings, while for others, it can take a $1 million nest egg or more. But no matter what savings goal you set for yourself, there's one important step to take on the road to building wealth -- start early.

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Let compounding work its magic

When you invest the money in your IRA or 401(k) plan, you get an opportunity to generate strong returns in your account. And the more years you give yourself to save and invest, the more opportunity you'll have to keep reinvesting those gains.

In fact, let's imagine you invest your savings heavily in stocks -- a smart thing to do when you're looking at a decades-long savings window. Let's also assume that your IRA or 401(k) manages to generate an average annual 7% return, which is a few percentage points below the stock market's average.

If you contribute $400 a month to your retirement plan, here's what your ending balance might look like, depending on how many years you give yourself to save and invest:

Savings Window

Ending Balance

20 years

$197000

25 years

$304,000

30 years

$453,000

35 years

$664,000

40 years

$958,000

45 years

$1.37 million

Table and calculations by author.

Now to give yourself a 45-year savings window, you'll effectively have to start funding a retirement plan from the start of your career through the end of it. But take a look at the gains you'll enjoy if you go that route.

Contributing $400 a month to a retirement plan over a 45-year period means putting in $216,000 in total. That means that in the example above, you're looking at a gain of over $1 million. And that's the power of compounded returns.

But the shorter your savings window, the less of a gain you get to enjoy. Even if you sock funds away in a retirement plan over 40 years and wind up with an ending balance of $958,000, that's still only a gain of $766,000 when you consider that it'll take $192,000 in out-of-pocket contribution to reach that point. And while $766,000 in gains is by no means shabby, it's not the same thing as seeing a gain of over $1 million in your account.

Get started as early as possible

The lesson here is that the more time you give yourself to save and invest for retirement, the wealthier you're apt to wind up. And if you've already been working for years but have yet to fund an IRA or 401(k), worry not.

In that case, you may need to contribute a larger sum of money each month to reach your savings goals. But if you make an effort to ramp up your savings rate, you may be surprised at how easy it is to make headway.

One final thing: The numbers you're seeing above apply to a retirement plan that's invested heavily in stocks. If you play it too safe with your investments, you might fall short on meeting your goals because you won't see such high returns.

Investing in stocks may fall outside your comfort zone, and if so, there are steps you can take to ease your fears. But it's important to invest your savings aggressively if you want to close out your career with a giant pile of cash.