Remembering one simple compounding rule can take years of worry about retirement off your mind, provide a clear goal in your financial life, and set you on a strong course for your later years. The rule: Your money will double every seven years if it compounds at the stock market's average return of nearly 11% annualized over its lifetime.

What does this mean? In simplest terms for this discussion, it means that if you have $125,000 in retirement savings by age 40, your money could grow to $250,000 by age 47, $500,000 by age 54, and $1 million by age 61. And that's without adding any additional money after 40.

Many people working today don't have pensions and will be self-reliant for most of their retirement income, so reaching a savings goal is of great importance. Hopefully, most of you over 40 have saved or are saving enough, and those of you under 40 are on course to save enough. If not, there's time to catch up -- even if the very young have it easiest.

Do the math
Assuming most of us start working around age 22, we have a good 18 years to reach $125,000 in retirement money by 40. Starting at 22, you need to save $6,950 a year to reach this savings goal. By putting the maximum $3,000 in an IRA annually (and the limit will increase to $4,000 in 2005), you're already nearly half there each year.

Saving at least 10% in your company's 401(k) plan would, on average, put you at or above the $6,900 a year hurdle. (Always save as much as your company matches -- it's free money -- and consider saving at least 10% of your pre-tax income after you've contributed to an IRA each year.)

So, by contributing the limit to an IRA annually and saving 10% of the average income, by age 40 a typical person starting at 22 will save more than enough to retire a millionaire at 60, even if they stop saving at that point, which is unlikely. (And this example doesn't assume any appreciation on all those 18 years of savings. Assuming 11% annualized returns over 18 years, saving $6,950 a year becomes $420,000 by age 40. So, saving just $2,000 a year from 22 to 40 will result in having $125,000 by age 40 given 11% appreciation.)

If you're 30 and just starting, you're still in good shape, too. Maxing out an IRA (preferably a tax-free Roth) will mean you're saving $3,000 a year, and 4,000 starting in 2005 (and double that for a couple). Then, by contributing a bit more generously to a 401(k) (15% to 20% of your pre-tax income -- and you might be surprised how little difference increasing your pre-tax 401(k) contribution makes to your final paycheck), on average, a 30-year-old making $45,000 a year would save $125,000 for retirement by their early 40s. That's enough to compound to a million by their early 60s.

Compounding is your friend
These examples don't account for inflation (which is very low but could change), taxes on 401(k) accounts, or the fact that the stock market could gain less than its past 80-year average.

But the examples also don't account for the fact that most of us will save well into our 40s and onward, and the money compounds as we save it. These things should largely balance each other out. The overall point here is to have a clear numerical savings goal for retirement accounts that you control, monitor, and root for.

To recap: If you have $125,000 in retirement savings by your early 40s (it needn't be 40 exactly -- most younger people today could work well into their 60s, and won't receive Social Security until 67), that money alone should grow to $1 million by your 60s.

So, where to invest the money? For most of us, low-cost index funds -- which outperform a majority of mutual funds and guarantee the stock market's return -- are the simplest, best choice. There's a lot to be said for simplicity. It works.

Jeff Fischer reminds you that in retirement you'll pay less for movie tickets, too. Bravo! The Fool has a disclosure policy .