It's probably not impossible for you to become a millionaire. Photo: Jericho, Wikimedia Commons.

We all would like to be millionaires -- well, except for those of us who happen to be billionaires. It's easy to imagine that it's an impossible goal; but it really isn't for many, if not most, of us.

You might achieve the goal through a delightful inheritance, or by beating odds of tens of millions to one and winning a lottery jackpot. Don't count on either of those, though. Instead, put a Roth IRA to work for you.

Roth vs. traditional IRA
There are two main kinds of IRAs: the traditional and the Roth. With a traditional IRA, you contribute money on a pre-tax basis. The value of your contributions is subtracted from your taxable income, so it reduces the tax you pay now. (For example, if your taxable income is $60,000 and you contribute $5,000, your taxable income falls to $55,000, shielding $5,000 from tax in your contribution year.) The money grows tax-deferred until you withdraw it in retirement, when it's taxed as ordinary income.

The Roth IRA is different in a few respects. It accepts only post-tax contributions, so you get no tax break up front. (Taxable income of $60,000 and contribution of $5,000? Your taxable income is still $60,000.) But if you follow the rules, you can withdraw the money in retirement completely tax free. It also imposes no required minimum distributions starting at age 70 1/2.

Image: Enkhtuvshin, Flickr.

The IRA contribution limits for both Roth and traditional IRAs are the same for both the 2014 and 2015 tax years: $5,500 -- plus an extra $1,000 "catch-up" contribution for those age 50 or older.

The millionaire-making power of the Roth
The miracle of compounding is what can make money grow more and more briskly over time. Imagine a sum, say $10,000, growing by 10% annually, for example. In the first year, it's 10% bigger, increasing by $1,000, to $11,000.

In the second year, that $11,000 grows by 10% -- which is now $1,100 -- and you end up with $12,100. The year after, that result grows by 10% ($1,210), becoming $13,310. The point here is not only to see how, in just a few years, your initial $10,000 is growing -- but that the amount by which it's growing is growing, too! First $1,000, then $1,100, then $1,210, and $1,331.

The Roth IRA can make the compounding effect even stronger for you, because it takes taxes out of the equation. The money you contribute is post-tax money -- but it grows and gets withdrawn tax free. Let's see how the growth happens with a few scenarios.

The table below shows you how much you can accumulate if you contribute $5,500 per year for 10, 20, 30, and 40 years. It also shows you the difference that the average annual growth rate can make.

Growing at

For 10 years

For 20 years

For 30 Years

For 40 Years

8%

$86,050 

$271,826

$672,902

$1,538,976

10%

$96,421

$346,514

$995,189

$2,677,685

12%

$108,100

$443,843

$1,486,609

$4,725,283

The U.S. stock market has averaged about 10% annual returns over many decades; these numbers show what you can achieve with below-average, average, and above-average rates of return, because you can't know what your particular time period will deliver. Including bonds in your mix will likely lower your average return, too. Still, it's clear that you can accumulate a million dollars if you have a few decades in front of you.

Perspective
If you don't have a few decades in front of you, or are just impatient, remember that the contribution limits for IRAs increase over time, and are adjusted for inflation. So, you'll be able to contribute more than $5,500 per year for most of those years.

You can also invest additional sums in other accounts. Moreover, if you already have $50,000 or $100,000 or $250,000 in accumulated wealth, getting to a million will be even easier and faster.

Remember, also, that in order to achieve the market's average return, you'll probably want to invest in a low-cost broad-market index fund, such as the SPDR S&P 500 ETF, Vanguard Total Stock Market ETF, and Vanguard Total World Stock ETF. Respectively, they distribute your assets across 80% of the U.S. market, the entire U.S. market, or just about all of the world's stock market.

You can aim to beat the market by carefully selecting individual stocks, but that will take time and skill. If you're interested in that, perhaps divide your investments between index funds and individual stocks. Just remember that it takes more than vast sums of money to become a millionaire; it takes perseverance, too. A Roth IRA can help you get there, building a comfortable retirement.