The all-purpose plastic bank card -- accessing a credit line, allowing cash withdrawals and debiting purchases against a bank balance -- may become a reality by the end of the decade, according to a new study by Payments Systems Inc. of Tampa, Fla.

The poll of 2,700 consumers, merchants and financial institutions was presented today at the annual convention and exposition of the Electronic Funds Transfer Association. The delegates here, over 1,000 strong, are high on hardware and hopes for the future.

It took 20 years for bank credit cards to reach a 30 percent penetration of the market and 10 years for 25 percent of all bank customers to use automated teller machines. Now the electronic soothsayers are predicting it will be about seven years before the world sees the generic plastic card enjoying universal access and acceptance.

For this to occur, the consumer must be "coached, coddled and convinced," according to Lawrence F. Linden, vice chairman of the board of the EFT association. "The consumer, not technology, will make or break EFT," he said.

Many speakers at the EFT convention said the customer does not perceive the need for a super card if it means taking away check "float." But a recent study by the Bank Administration Institute revealed that only about one-third of customers polled value the float. More people, it turns out, fear fraud and computer glitches, and only 15 percent would be interested in paying for such a service, said Peter Bryan of Madison Consulting Group of El Segundo, Calif.

The subject drawing the largest interest at the convention was the point-of-sale transaction. This refers to making a purchase at a retail outlet with a card that automatically deducts the amount of sale from the customer's account and credits it to the merchant.

Point-of-sale, or POS, made its debut in the 1970s. It flopped, largely due to poor marketing by the banks offering it, one banker admitted. But in the past two years, POS has revived, thanks to the spread of automated teller networks and the efforts of oil companies that saw in POS a means to reduce the costs of credit card purchases of gasoline. Shell Oil's manager for field systems and programs, Robert Jensen, reported that the company now has 3,225 terminals at service stations, and where present, 80 percent of the sales are registered on those machines.

But POS has not yet caught on with other retailers. Besides the lack of consumer demand, there are technical and legal issues still to be resolved, as well as large development costs for a system that would appear as yet to have little economic justification. Nevertheless, a few merchants are cautiously moving ahead. Safeway Stores plans to begin a pilot program later this year.

Woodward & Lothrop, which started development in early 1983 only to be set back by the decision of local banks not to issue Visa Electron cards, is renewing its efforts with the regional ATM network called Internet. Senior Vice President Joseph Gallucci detailed many outstanding problems, such as the personal identification number needed to use the debit card. If the problems are eliminated, he said, a pilot program could begin in six months.

To make POS a success, retailers and financial institutions will have to share the cost equitably in the beginning, said PSI's executive vice president, Allen R. DeCotiis. Moreover, he said his survey showed that customer participation would double if cash discounts of as little as one or 2 percent were offered.

Another EFT area, home banking -- the use of a personal computer to get balance information, pay bills or transfer funds -- remains more promise than reality. "It hasn't taken off the way we thought it would," said Charles Forbes, Chemical Bank's vice president in charge of its Pronto System. Eighteen months after its inauguration and with $150 million spent on development, Pronto and similar systems introduced by BankAmerica Corp. and other large money center banks have only 50,000 users so far. Videotex -- of which home banking is a part -- is "a solution looking for a problem," a Los Angeles banker said. "We know how to send information; we don't know what information people will pay for."

The number of households with personal computers had been projected to increase from the current 11 percent now to 40 percent in 1990, but recently sales have slowed. So banks are being urged to shift marketing emphasis away from consumers toward small businesses that would be willing to pay $50 to $100 a month for services.