If investing feels rather intimidating, don't let that stop you from starting, or at least beginning to learn how. That's because over the long term, equities, on average, are almost certain to appreciate, and they grow much faster than inflation rises. Keeping your savings in a bank -- especially at today's rock-bottom interest rates -- is almost certain to erode your wealth due to inflation. For a stress-free retirement, you'll need to invest early and often.

If you're intimidated by trying to pick stocks yourself, fear not. You can choose from many actively managed mutual funds and low-cost passive index funds that can give you diversified exposure to a broad index of equities.

However, it can also pay to invest a portion of your savings in individual stocks, because winning growth stocks can go on to beat the broader market by staggering amounts. In fact, investing in one of the top stocks in the world at a relatively early stage has the potential to fund your entire retirement.

Don't believe me? Here are three examples of stocks that turned just $1,000 into a cool million bucks -- and even more.

A man smokes a cigar in his deck chair from a high vantage point overlooking a city at night.

These three companies have made investors 1,000 times their money. Image source: Getty Images.

Amazon

In perhaps the greatest feat of modern business, e-commerce and cloud computing giant Amazon.com (NASDAQ:AMZN) has turned $1,000 into more than $1 million in just 22 years as a public company. Founded as an online bookseller by Jeff Bezos in the early days of the internet, Amazon has expanded its reach into virtually every aspect of the consumer and business economy. From books, the company went on to offer a much wider range of goods and services, with as much depth of inventory, value, and delivery speed as possible, in order to delight customers.

In an unconventional turn, Amazon's management decided to eschew dividends or buybacks after the company's initial success. It chose instead to reinvest all profits back into the business: building more infrastructure, extending the company's first-mover advantages in e-commerce, and inventing new products and services.

These have led to several huge businesses, including the Prime subscription program that now offers free one-day shipping and access to Amazon's award-winning Prime Video catalogue. Amazon is now also becoming a threat in digital advertising, a segment that's expected to exceed $11 billion in revenue for the company this year.

But the most consequential Amazon "invention" is Amazon Web Services. By developing a way for companies to outsource their computing and storage needs to Amazon's hyperefficient data centers, AWS pioneered the cloud computing revolution, which is disrupting the highly profitable enterprise computing and software spaces. From a standing start in the mid-2000s, AWS is now a business with a run rate of $36 billion, growing at 35%, and with operating margins between 25% and 30%.

Amazon has been able to achieve and maintain this success by adhering to the business principles set forth in Bezos' first 1997 letter to shareholders: He preached focusing on the long term rather than short-term profits, not being afraid to experiment, and obsessing over customers above all else.

The results? After going public in 1997 at $18 per share, Amazon.com split its stock three times (twice 2-for-1, and once 3-for-1), for a split-adjusted IPO price of just $1.50. At today's stock price of roughly $1,850 per share, that equates to a return of 123,200%, turning $1,000 into $1.23 million today.

Microsoft

The other cloud computing giant besides Amazon is Microsoft (NASDAQ:MSFT), another company that's turned $1,000 into more than $1 million. Of course, the cloud wasn't Microsoft's primary business. After its founding in 1975 by Bill Gates and Paul Allen, Microsoft's first winning product was an operating system for the earliest personal computers.

Microsoft later released its flagship product, the Windows operating system, in 1983; it would go on to sell Microsoft Office, the dominant software suite for all kinds of business tasks, beginning in 1989. Subsequent releases included the Internet Explorer web browser in 1995, the Xbox video game system in 2001, and the Microsoft Surface laptop and tablet in 2012.

However, Microsoft's most consequential modern product is its Azure cloud computing service, now a strong No. 2 to AWS in the cloud computing space. The cloud unit was helmed by executive Satya Nadella, who assumed the CEO role in 2014 and has led a renaissance in Microsoft's growth prospects ever since. Nadella also led the acquisition of LinkedIn in 2016, a purchase that looks savvier by the day, putting the leading business-oriented social network under Microsoft's corporate umbrella.

Though Microsoft initially went public in 1986 at $21 per share, the stock has split many times, and its split-adjusted IPO price is a mere $0.072 (just over seven cents). That means at today's share price of around $157, Microsoft stock has appreciated 217,900%, turning $1,000 into $2.18 million over 33 years.

Berkshire Hathaway

Finally, let's look at Berkshire Hathaway (NYSE:BRK.A) (NYSE:BRK.B), the financial conglomerate founded by Warren Buffett. The company got its start when Buffett, a successful investment-fund manager, took a controlling stake in declining New England textile business Berkshire Hathaway in 1964. Fortunately, Buffett and partner Charlie Munger soon realized the textile business had subpar long-term prospects; they pivoted, taking the cash flow from Berkshire and diversifying into the insurance business.

Buffett and Munger then took the insurance "float" -- premiums received before liabilities have to be paid out -- and used their value investing skills to buy shares of high-quality equities and to buy entire companies outright. This was an innovative, and slightly riskier, way to invest insurance float, which traditional insurers usually put into lower-risk bonds.

However, Buffett and Munger, two of the best investors of all time, picked several gigantic winners over the subsequent years and decades. These included GEICO and See's Candies, both of which Berkshire now wholly owns; Coca-Cola in the 1980s; several highly profitable bank investments after the financial crisis of 2008; and even a foray into technology, with a successful 2016 investment in Apple.

Not only do Buffett, Munger, and Buffett's two lieutenants Todd Combs and Ted Weschler invest the float from Berkshire's large and diverse insurance operations -- but under the guidance of insurance head Ajit Jain, most of Berkshire's insurance operations themselves are quite profitable, even before investing the gains. This combined team and business model has allowed Berkshire's market value to compound over 20% annually for 55 years, a stunning achievement for that amount of time and for a company so large. These gains have enabled Berkshire Hathaway's stock to increase roughly 2,700,000%, turning a mere $1,000 investment in 1964 into a stunning $27 million fortune today.

What made these stocks big winners?

What are the common characteristics of these incredible winners? All three companies were founded and run by bona fide geniuses: Buffett, Bezos, and Gates. Those geniuses were also master capital allocators, aggressively reinvesting most of their profits to further strengthen their business moats, and then creating new high-return businesses -- some quite different from their companies' original products or services.

After all, Windows is now an afterthought for Microsoft investors, who are more focused on Microsoft's cloud and other software products. Many Amazon investors think most of the company's value is now tied up in AWS, third-party services, and advertising, not its original direct e-commerce operations. And Berkshire Hathaway shut down its textile operations in 1985, keeping only the name of the original mill.

Thus, the right formula for massive investment gains seems to be: Identify geniuses with the right business models, and the freedom to reinvest in new businesses and services as they see fit; have the faith to hold your money with them over the course of years and decades.

Of course, there aren't many business geniuses out there with the right open-ended business opportunities. But if you think you've found one, don't hesitate to invest. As these three companies have shown, a small investment can go a very long way.