The company markets so-called prepaid debit cards, which look and act like bank debit cards. But prepaid cards don’t pull money out of your checking account. Instead, consumers load them with their own money — using cash or direct deposit of their paychecks.

“We call it the Southwest Airlines of bank accounts. It’s simple, it’s easy, and the fees are transparent,” Steven W. Streit, founder and chief executive of Green Dot, said Thursday.

The firm’s shares soared $7.99 to $43.99 on Thursday, up 22% from their higher-than-projected price of $36 in the initial public offering late Wednesday.

The offering raised about $187 million, but none of that went to Green Dot. All of the shares bought in the offering were sold by existing stockholders in the company.

Green Dot is the largest player in the prepaid debit-card industry, with about 3.4 million active cards. The No. 2 provider is NetSpend Holdings Inc. of Austin, Texas, which also intends to go public.

Industrywide, money loaded onto general-purpose reloadable debit cards in the U.S. will soar to $118.5 billion in 2012, up from only $8.7 billion in 2008, research firm Mercator Advisory Group estimates. That figure could reach $440 billion by 2017, Boston Consulting Group projects in a report prepared for MasterCard.

Most Americans are familiar with prepaid debit cards mainly as gift cards, an easy way to pay for those lattes at Starbucks until the cash stored on the plastic runs out.

But prepaid cards also can be souped up for use at any place that accepts MasterCard and Visa — with which Green Dot has partnerships — as well as for such applications as paying bills online.

A consumer can grab a card from Green Dot or one of its retailer partners while waiting in a checkout line and pay as much as $4.95 each time it is loaded with cash. There is no reload fee for direct deposits of paychecks. One catch: There is a $5.95 monthly maintenance fee, but it is waived each month that the card is used at least once a day on average, even if only to buy a pack of gum at a time.

Green Dot posted $235 million in revenue for the fiscal year that ended in July 2009, up 40% from the year before. Its earnings more than doubled to $8.2 million. That rapid growth slowed in the first few months of the current fiscal year but remained quite strong.

Green Dot garners 64% of its revenue as the provider of prepaid debit cards for Wal-Mart Stores Inc., which took a small stake in the Monrovia company recently. It also sells cards online and through retailers including CVS, Kroger, Rite Aid, Walgreens and 7-Eleven.

The cards also are used for many specialty purposes, such as paying a doctor through a healthcare spending account.

Major employers including Wal-Mart are using the cards to pay employees, and big banks are teaming up with the government to issue the cards for Social Security payments and other federal disbursements.

The government cards can be fine-tuned so that, for example, a recipient could use them to buy regular groceries but not beer and cigarettes, said Zil Bareisis, a consultant in London with Oliver Wyman Group’s Celent unit.

For now, the biggest market is people outside the financial mainstream, including those who may have given up on banks because they were socked with huge overdraft charges or can’t maintain a high-enough balance or use enough additional bank services to qualify for free checking.

“The unbanked represent a huge customer base and opportunity,” said Mayank Tandon, a financial technology analyst with Signal Hill Capital Group in Baltimore. “They are really the target for the prepaid cards.”