Are you looking to get rich on a budget? You're not alone. And, good news! Lots of self-made millionaires became wealthy not because they made tons of income, but because they invested wisely. You can do the same.

You don't need to be a stellar stock-picker to do so either. In fact, investing $100 per month in one simple exchange-traded fund (ETF) will do the trick. The only catch? You need to be able to make this monthly investment for at least 45 consecutive years.

That may be more doable than you think though.

Simpler is better

The ETF that will get you from nothing to a seven-figure stash in a mere 45 years? It's not a high-flying tech fund. It's not an ETF that employs a complicated "black box" trading strategy either. Rather, it's the SPDR S&P 500 ETF Trust (SPY -0.27%) -- an exchange-traded fund meant to merely mirror the performance of the stock market's primary benchmark index, the S&P 500 (^GSPC -0.24%).

To relatively new investors the suggestion seems outrageous. The whole point of being an active investor is to outperform the stock market! Just matching the overall market's gains isn't a particularly impressive feat.

As most veteran investors can attest, however, consistently beating the market is a rarity. Most mutual fund managers can't even do it. It's at least as tough for individual investors with full-time jobs and fewer resources to do so. Besides, as the math and graph below will show, the boring ol' S&P 500 or any of its index funds are up to the task of making almost anyone a millionaire.

But first things first: There are three assumptions that need to be made before we get to the math.

First, for the purposes of our growth calculation we'll assume the S&P 500 will dish out an average yearly gain of 10%. Some years are worse, and others are better. In some years the S&P 500 even loses value! Generally speaking though, this is the broad market's average annual return going back the past 100 years. If you stick with your investment in the SPDR S&P 500 ETF Trust for a full 45 years (and barring any fundamental changes to the way the global economy or the stock market functions), you should achieve pretty similar returns.

The second assumption I'm making with this number-crunching is you're not paying any taxes while you're adding money to the investment every month and/or while it grows, as would be the case with a traditional IRA. You wouldn't start paying taxes on any of this money until you start selling the position and taking the money out of the account.

And the third assumption? Reinvesting any dividends the ETF might pay while you're holding it.

Here's the visualization of your monthly contributions and their net cumulative growth over the course of 45 years, which ends with a value of just over $1 million.

As you can see, the seemingly slow start really starts to accelerate about two-thirds into the 45-year stretch. That's when you've finally got enough in the account to start making some real money on your savings. The hard part is sticking with the plan long enough to reach that point.

You want more? Stick with the same plan for seven more years and you'll have over $2 million.

There are a couple of things to know about the visualization above. First, while for the purposes of this illustration the account's value moves in a relatively smooth line from left to right, your experience won't be the same. Although you'll still more or less end with the same $1.05 million (or $2.1 million with the 52-year plan), your account's value will ebb and flow with the market. As was noted, while some years are better than others, a handful of years are downright lousy.

Second, although $1 million is a decent retirement stash now, that may not be much money 45 years from now.

On the other hand, as your income grows over the course of the coming 45 years you should be able to invest more than $100 on a monthly basis. If you can crank that monthly contribution up to just $200 within a couple of decades you'd be able to shave a few years off that accumulation period. Ditto for the 52-year plan to reach the $2 million mark.

Time does most of the heavy lifting

Still... 52 years, or even just 45 years? Both are a long time!

Except, it isn't quite as long as the number itself sounds like it is. If you can start socking $100 per month away when you're 18 years old, you'd be able to stop contributing and start living on this money at the relatively young age of 63. If you're aiming for $2 million, you'd be waiting until you're 70.

The bigger lesson to learn here, however, is one of time. Time is your biggest ally when it comes to successful investing. It can overcome relatively modest income during your working years. Conversely, even with an above-average income later in life it can be tough for an investor to make up for lost time. As the chart above shows, there comes a point when your cumulative investment starts generating far more in yearly gains than you could ever contribute to the account from your work-based wages. The sooner you get to that point, the better.

Perhaps more than anything though, recognize that it's possible to eventually become rich even with the smallest of starts. Just begin when you can with what you can. Even if you're not on track to reach multimillionaire status you'll still be far better off than you would be doing nothing.