You can make a lot of money by investing in stocks if you have two things. It takes money to make money, so you'll need funds to invest first and foremost. You also have to know which stocks to invest in. Not every stock has what it takes to be a big winner.

The good news is that it doesn't take a huge amount of money upfront to invest. The even better news is that there are plenty of great stocks you can purchase that are likely to deliver tremendous gains over the long run. If you've got $5,000 to invest, buying these three growth stocks could make you a fortune.

Smiling young person holding palms up as cash rains down.

Image source: Getty Images.

1. Square

Think about the following scenario. The U.S. is mired in a recession. A global pandemic has turned the retail market upside down. Yet Square (NYSE:SQ), a company whose fortunes in the past have been intertwined with the overall economy and retail strength, reported blowout third-quarter results earlier this month. 

How has Square performed so well during challenging times? Largely because of the impressive momentum for its Cash App peer-to-peer payment app. The pandemic has accelerated the shift from cash to digital payment methods like Cash App. This trend is likely to continue for years to come, driving sustained growth for Square.

Don't overlook the company's other products and services, though. Square is best known for its credit card readers used by sellers, but it offers an entire ecosystem that supports merchants' businesses. This ecosystem includes payroll services, e-commerce sites, loyalty programs, business debit cards, and more. This depth of products and services makes Square very "sticky" to its customers.

Square's seller ecosystem continues to grow even with the pandemic still under way. But the pandemic will end sooner or later. When it does, expect this business to fuel even more growth for Square. 

2. Teladoc Health

The COVID-19 pandemic has served as a major catalyst for Teladoc Health (NYSE:TDOC). The telehealth services provider's business is booming thanks to the soaring number of visits spurred by the coronavirus outbreaks.

However, Teladoc's momentum isn't likely to end when the pandemic does. Telehealth is here to stay. It's convenient for patients and more cost-effective for employers and health plans. In addition, some specialties are especially well suited for telehealth. Demand for Teladoc's dermatology and behavioral health services, for example, is growing much faster than its other specialties.

Teladoc recently completed its acquisition of Livongo Health. This deal brought Livongo's digital health management platform for chronic conditions under Teladoc's umbrella. The combination of the two companies means that Teladoc now has an addressable market of over $120 billion in the U.S. alone.

The telehealth company's opportunity isn't limited to just the U.S., though. Teladoc has a global presence already. And it recently launched a partnership with Telefonica, which ranks as one of the top telecom providers in Europe and Latin America. Telefonica will distribute Teladoc's virtual care offering initially in Spain, but the two companies could eventually work together in other markets.

3. Trupanion

There are around 180 million cats and dogs in North America. Pet ownership is growing, in part due to individuals working from home because of the pandemic now enjoying more freedom to get a pet. Trupanion (NASDAQ:TRUP) is well positioned to benefit from this trend as the leading provider of medical insurance for cats and dogs.

Pet medical insurance hasn't been as widely adopted in the U.S. and Canada as it has in other major countries. For example, 40% of pets in Sweden are covered by medical insurance. Roughly 25% of pets in the U.K. are protected by medical insurance.

Trupanion estimates that its potential market in North America would top $32 billion annually if it can achieve the same level of market penetration that already exists in the U.K. However, the company doesn't have to come close to that goal to still have a tremendous runway for growth.

The prospects of accelerated growth for Trupanion appear to be greater than ever now thanks to a major partnership with large supplemental insurance company Aflac. The two companies recently reached a deal in which Aflac will market Trupanion's products in the U.S. and explore opportunities in Japan. Aflac also invested $200 million in Trupanion, a clear sign that the big insurer believes in the potential of pet medical insurance. 

An important thing to note

Investing $5,000 in Square, Teladoc Health, and Trupanion stocks could very well make you a lot of money over the long run. However, there's one important thing to note: You'll need to hold onto the stocks rather than sell them after a quick gain (which they're quite capable of delivering). The main attraction of each stock is its long-term potential. Selling too soon could limit your returns.

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.