Make money. That's every investor's goal. How each person chooses to achieve that goal makes the difference in exactly how much money they make and how long it takes to make it.

Some stocks are better vehicles than others for making a lot of money in a relatively short period. If you've got $500 to invest, here are three growth stocks that could double your money.

1. Axsome Therapeutics

You can buy one share of Axsome Therapeutics (AXSM 0.88%) right now for less than $75. I think investing in this biotech stock should pay off in a big way over the next few years.

Axsome already has two products on the market. It won U.S. regulatory approval for Auvelity last year as a treatment for major depressive disorder. The company also picked up commercialization rights for sleep-disorder drug Sunosi from Jazz Pharmaceuticals in 2022.

Sunosi could generate peak sales of several hundred million dollars. But Auvelity is poised to become a blockbuster, with GlobalData projecting peak sales of $1.7 billion.

That's just the tip of the iceberg for Axsome, though. The company expects to file for regulatory approvals for AXS-07 in treating migraines and AXS-14 in treating fibromyalgia later this year. It's also pursuing additional indications for Auvelity (AXS-05) and Sunosi (solriamfetol).

Axsome's market cap currently stands at around $3.5 billion. With the tremendous potential for Auvelity and the company's promising pipeline, it's not hard to envision the stock doubling or more by the end of the decade.

2. Brookfield Renewable

Most companies don't lay out the details of how they can double investors' money. But Brookfield Renewable (BEP -0.92%) (BEPC -0.31%) isn't like most companies.

Brookfield Renewable isn't shy about telling shareholders that it expects to deliver average annual total returns of between 12% and 15%. Hitting the low end of the range would double your investment in a little over six years.

How does Brookfield Renewable plan to achieve this target? By scaling up to meet the growing demand for renewable energy. Getting to net-zero carbon emissions (as countries around the world seek to do) will require four times the level of wind and solar electricity generation produced in 2020. Brookfield Renewable's development pipeline capacity is, not coincidentally, roughly four times its current operational capacity.

The renewable energy leader has proven it can deliver on its targeted returns in the past. Brookfield Renewable's total return since 1999 averaged 16% per year. 

You can invest in Brookfield Renewable in a couple of ways. Its limited partnership trades under the BEP ticker with a share price below $30. Its corporate entity trades under the BEPC ticker with a share price of less than $32.

3. Vertex Pharmaceuticals

It isn't just small companies, like Axsome Therapeutics and Brookfield Renewable, that have the potential to deliver 2x returns. I think that big biotech Vertex Pharmaceuticals (VRTX -0.51%) also has what it takes. You can buy one share of Vertex for under $350.

The key for Vertex to grow much larger is for the company to expand beyond cystic fibrosis (CF), an indication in which it currently has a monopoly. Vertex is poised to take the first major step with regulatory approvals in the U.S., European Union, and U.K. for exa-cel in treating sickle cell disease and transfusion-dependent beta-thalassemia.

Exa-cel, though, is only the first of three non-CF blockbuster candidates that Vertex could launch over the next few years. The company expects to complete late-stage clinical studies evaluating non-opioid pain drug VX-548 by early 2024.

It's also testing inaxaplin in a pivotal clinical trial targeting APOL-mediated kidney disease. This indication affects more patients globally than CF. There are no currently approved therapies that treat the underlying cause of the disease.

Those programs could be enough to make Vertex stock double over the coming years. However, the company also could launch its most powerful (and likely most profitable) CF therapy in the not-too-distant future. It's advancing a potential cure for type 1 diabetes in early-stage testing, as well.