Don't let anyone tell you that you must have a boatload of money to get started investing in stocks. It's simply not true. Sure, you'll need some upfront cash. However, even a modest amount is enough to scoop up shares of some companies with exciting prospects.

Got $200? That's more than you'll need to buy these three growth stocks that could double your money.

1. Axsome Therapeutics

Biotech stocks are often volatile. But they provide one of the best opportunities around to achieve 2 times or greater returns in a relatively short time. I think that Axsome Therapeutics (AXSM -1.20%) has the potential to deliver on that goal -- and its stock costs less than $70 per share.

Axsome's share price has dropped year to date. That's mainly because of two factors. The company conducted a $225 million public-stock offering in June, which diluted the value of existing shares. It also pushed back on the time line for resubmitting for U.S. approval of AXS-07 in treating migraines and added some wiggle room in its expected filing for approval of AXS-14 in treating fibromyalgia.

However, the positives for Axsome outweigh the negatives, in my view. The company's flagship product, Auvelity, continues to pick up strong momentum in treating depression after winning U.S. approval a year ago. Jefferies analyst Chris Howerton has predicted that the drug could generate peak annual sales of up to $1.8 billion.

Axsome also markets sleep-disorder drug Sunosi, which it acquired from Jazz Pharmaceuticals. Its pipeline includes the aforementioned AXS-07 and AXS-14 plus experimental narcolepsy drug AXS-12. In addition, the company is evaluating Auvelity and Sunosi in treating other indications.

I don't think the market is giving Axsome's products and pipeline enough credit. Its market cap currently stands at around $3.3 billion. My hunch is that continued success for Auvelity and Sunosi along with a couple of regulatory wins could propel this stock much higher.

2. Beam Therapeutics

You can pick up a couple of shares of Beam Therapeutics (BEAM -2.69%) after buying Axsome stock and still have money left from your initial $200. Beam is a high-risk yet potentially high-reward proposition.

The company is pioneering the use of base editing in developing therapies. Base editing is a type of gene editing that is superprecise and doesn't make unwanted off-target edits that can be problematic with some other approaches.

Beam doesn't have any approved products yet, but it's making progress. It's evaluating BEAM-101 in a phase 1/2 clinical study for treating sickle cell disease. BEAM-201 is in a phase 1/2 study targeting T-cell acute lymphoblastic leukemia/T-cell lymphoblastic lymphoma. The company plans to file in the first half of 2024 for authorizations to advance BEAM-301 and BEAM-302 into clinical testing for treating two rare genetic disorders. 

These initial programs could be just the tip of the iceberg. If Beam demonstrates that base-editing therapies are safe and effective, it could pursue other treatments for a wide range of diseases. There's no guarantee of success, but it's possible that Beam could deliver gains much greater than 2 times over the next several years.

3. Brookfield Renewable

Biotechnology isn't the only area where you can double your money. Renewable energy is another hot industry. For less than $30 per share, you can invest in one of the top renewable-energy leaders -- Brookfield Renewable (BEP -2.42%) (BEPC -1.10%).

Brookfield Renewable can currently generate around 32 gigawatts of electric power. It operates hydroelectric, wind, solar, and distributed energy facilities on four continents. But the company is preparing to deliver a lot more renewable power: Its development-pipeline capacity totals roughly 132 gigawatts.

The demand for renewable energy will almost certainly climb significantly in the coming year. Concerns about climate change have spurred countries and major corporations to embark on aggressive carbon-emissions reduction programs. It also helps that wind and solar are now more cost-effective energy sources than fossil fuels.

Brookfield Renewable has provided an annualized total return of 16% since 1999. The company expects to generate average-annual total returns going forward of between 12% and 15%. That's enough to double an initial investment within five to six years.