So you want to retire a millionaire. That may seem like a lofty goal, but it's far from an unreasonable one. These days, even a million dollars won't be enough for many people to enjoy the retirements they hope for. If you use the flawed (but still insightful) "4% rule," it would have you withdraw 4% of your nest egg in your first year of retirement, adjusting your withdrawals upward in the years that follow to account for inflation. And 4% of $1 million is just $40,000.

The average annual Social Security retirement benefit is around $22,000. Even if you collect $30,000, adding that to $40,000 only gets you $70,000. See? That's not anywhere close to a lofty income level. Here's a look at how you might amass a $1 million nest egg (or a bigger one!) before you retire.

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Image source: Getty Images.

Getting to a million is all math

Whether you have 10 years before you retire or 40 years, you'll need to be investing regularly and effectively. Much will depend on how much you can steadily sock away and on how quickly your portfolio grows.

It's hard to beat the stock market for long-term growth. The stock market has averaged annual returns of close to 10% over many decades, but its returns could be more or less than that over the particular period during which you're investing.

Here's what you might amass at different average annual compound growth rates if you sock away $10,000 annually:

Growing for

Growing at 6%

Growing at 8%

Growing at 10%

10 years

$139,716

$156,455

$175,312

15 years

$246,725

$293,243

$349,497

20 years

$389,927

$494,229

$630,025

25 years

$581,564

$789,544

$1.1 million

30 years

$838,017

$1.2 million

$1.8 million

35 years

$1.2 million

$1.9 million

$3.0 million

40 years

$1.6 million

$2.8 million

$4.9 million

Calculations by author. Growth is calculated on a compounding basis.

You can see what a big difference apparently small improvements in the growth rate make over time. Since no one is guaranteed a 10% return from stocks, let's focus on a scenario that's a little more conservative. The table below shows how much you might amass from a portfolio growing at an average annual compounded rate of 8%, investing $7,500 or $15,000 annually:

Growing at 8% for

$7,500 invested annually

$15,000 invested annually

5 years

$47,519

$95,039

10 years

$117,341

$234,682

15 years

$219,932

$439,864

20 years

$370,672

$741,344

25 years

$592,158

$1,184,316

30 years

$917,594

$1,835,188

35 years

$1,395,766

$2,791,532

40 years

$2,098,358

$4,196,716

Calculations by author. Growth is calculated on a compounding basis.

How to aim for 8% returns

If you want to chase high returns, you might invest in growth stocks, which are tied to companies growing at faster-than-average rates. This approach has more risk than just aiming for the market's average returns, so if you take it on, you'll want to read and learn more about it. You'll also do well to spread your dollars across a bunch of growth stocks, keeping up with them all at least quarterly.

Most people, though, would be better served by opting for a simpler approach -- investing in low-fee stock index funds, either in mutual fund or exchange-traded fund (ETF) form. Each will aim to deliver roughly the same returns as a specified index of stocks.

Top-notch Vanguard ETFs

Here, then, are three candidates for your long-term dollars from Vanguard, whose founder was an index fund pioneer. Among other things, Vanguard is known for low fees.

  1. Vanguard S&P 500 ETF (VOO 1.00%): S&P 500 index funds are among the most common, for good reason. They include as their constituents 500 of the biggest companies in America, which together make up around 80% of the value of the entire U.S. stock market.
  2. Vanguard Total Stock Market ETF (VTI 0.93%): It's reasonable to consider this ETF, too, because it aims to include all publicly traded U.S. companies on the major exchanges, including small and medium-sized companies.
  3. Vanguard Growth ETF (VUG 1.82%): This ETF has a great track record and offers a way to invest in large-cap growth stocks without having to expend much energy. It tracks the CRSP U.S. Large Cap Growth Index.

Here's how these funds have performed over the past five and 10 years:

ETF

5-year Average Annual Gain

10-year Average Annual Gain

Vanguard S&P 500 ETF

11%

10.9%

Vanguard Total Stock Market ETF

10.2%

10.2%

Vanguard Growth ETF

13.7%

12.6%

Source: Morningstar.com. 

Those are some exciting numbers, but they're not necessarily the returns you'll get in any future period. You could do worse -- or better. If you can't decide which one to invest in, you can always spread your long-term investment dollars across two or more of them.

Investing significant sums over many years can get you a nest egg worth hundreds of thousands of dollars -- or perhaps a million dollars, or more.