Successful investing is all about finding stocks that have the potential to appreciate in value and then holding on to them as they do.

That's why most investing styles revolve around some form of choosing stocks that are either in high-growth phases or that trade beneath their real value. In both of these cases, investors expect the value of the stock to increase over time.

One of the differences between growth investing and value investing is the stage of the company. Growth companies are typically new and developing. As a result, they're often not profitable, and therefore risky to hold, but they also offer the maximum potential for gains, which makes them appealing.

Ideal growth stocks have proved themselves enough that they're worthwhile bets, even though they may retain elements of risk. Airbnb (NASDAQ:ABNB) and Square (NYSE:SQ) have both demonstrated enormous relevance and stability, and they're both growing through the roof. These are stocks you can hold forever and expect to skyrocket.

Three people standing in a garden with suitcases.

Airbnb guests. Image source: Airbnb.

Airbnb: Disrupting travel

Airbnb stock rocketed 50% from its first-day closing price within two months of its IPO, but it's fallen far from there since. Even now, 26% off their February high, shares are trading at an outrageous 22 times sales. 

Perhaps that's justified not only by the travel company's recent performance, but by its potential. In the second quarter, Airbnb sales increased 299% year over year, making up for lackluster sales during the height of pandemic restrictions. Gross booking value increased 320%, and the net loss contracted year over year.

But it's only going to get better. CFO Dave Stephenson said that management is expecting record sales and profits in the third quarter. "People want to travel," he said, "and they are really resilient in finding ways to travel."

And Airbnb offers paths toward travel under challenging circumstances. That's why it was able to bounce back so phenomenally in Q2, and why investors can expect the company to crank out high growth going forward. It doesn't need to invest in costly building developments to provide more residences, but it can increase locations by bringing in more hosts. It also offers living quarters in remote locations, which traditional travel can't match, as well as better terms for longer stays, which contributed to higher sales in the second quarter. Even if those trends change, Airbnb's adaptive model means that it's likely to be able to support whatever the newest ways to travel are at any given time.

The high valuation means that investors may face volatility in the near future, but holding the stock long-term is a great bet for high gains.

Two people in a liquor store pointing at a Square point-of-sale tablet.

A Square point-of-sale device. Image source: Square.

Square: A fintech in motion

Square has been a hot stock for a while now, because it keeps launching new services and upgrading its business. This has led to a five-year return of more than 2,000% for Square stockholders. It hasn't stopped, gaining 24% year to date as of this writing, and it doesn't seem like it's anywhere near taking a break soon.

Square has two core businesses: its original sellers business, which provides payment and management solutions for small businesses, and Cash App, its peer-to-peer payments app, which now also offers stock and cryptocurrency trading. Bitcoin (CRYPTO:BTC) trading has powered a lot of recent growth, since Square counts it as revenue, especially last year when the sellers business suffered because of closed stores. But total revenue increased 143% year over year in the second quarter, with the sellers business's sales increasing 81%. Revenue increased 87% without Bitcoin.It's also posted three consecutive profitable quarters after a loss at the beginning of the pandemic.

The company made two important announcements in the past two months that should drive even more business. One is the launch of a highly anticipated banking app, which gives it more ways to make money. The other is the acquisition of Afterpay, a company that offers buy now, pay later services. These moves both chip away at traditional banking services and open up new streams of revenue for the company, which could become huge.

Investors can count on similarly big moves from Square in the future, making it a stock you can likely hold forever as it piles on more gains.

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.