American Express (AXP 3.57%) is a dominant force in the credit card industry, with premium offerings that support its brand recognition. It also runs a closed-loop payments platform, allowing it to benefit from a network effect. Warren Buffett certainly likes the business, as Berkshire Hathaway owns 21.8% of the outstanding shares.

But can this financial stock turn a $10,000 investment into $50,000 by 2030? Here's what investors need to know.

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Soaring throughout the rest of the decade

If American Express shares soared fivefold over the next five years, investors would register a fantastic 38% annualized return. That gain would certainly outperform the broader market.

However, it's best to temper expectations. With the utmost confidence, I can say that American Express stock won't turn a $10,000 investment into $50,000 by 2030. In the past five years, shares have generated a total return of 237%, which is still great, but well short of 400%.

This is an established business that won't put up monster growth anymore. Management expects earnings per share to increase at a mid-teens percentage pace over the long term.

Extend the time horizon for American Express

While betting on American Express shares to rise fivefold in five years is a losing proposition, all hope isn't lost. Investors who can lengthen their time horizon might see that kind of gain from this stock. I wouldn't be surprised to see a 400% return over a 15- or 20-year period, for instance.

The stock isn't cheap, though. Prospective buyers must be OK with paying a historically expensive price-to-earnings ratio of 21.6 to add American Express to their portfolios. This introduces a headwind to achieving even better returns.

This is an outstanding company. It's a strong brand, benefits from a network effect, and has the Oracle of Omaha's endorsement. It at least deserves a spot on the watch list for now.