The number of banks in the United States will shrink by a third, to 10,000, as a result of competition and mergers in the next five to seven years, a study by the accounting firm of Peat, Marwick, Mitchell & Co. predicts.

The study, being issued today in connection with the opening of the annual convention of the American Bankers Association in New York, also says there will be between 10 and 20 national financial service "retailers." Bank-like products are now being offered by a plethora of companies ranging from securities firms to retailers.

Half of all traditional full-service bank branches will be closed or modified, to be replaced by so-called support branches, says the study, "The Retail Force: Consumer Delivery Decisions for Financial Institutions." Instead of tellers, the support branch will be staffed by home banking representatives and will house communications centers and even computer stores.

An alternative scenario would find the spread of generic branches -- shared facilities belonging to several banks. These would offer automated teller machines, point-of-sale operations, night deposit boxes, direct-line telephones, applications and brochures, and video terminals, the report says.

"Many banks will have to follow this approach in order to retain customers, who will otherwise find it more convenient to buy their financial services where they buy their clothes and groceries," Peat Marwick says.

In the bank of the future, employes will become commissioned advisers and agents, offering financial planning, brokerage and home computer services. On the other hand, automated teller and point-of-sale machines dispensing cash and accepting payment will be ubiquitous because banks will offer incentives to use them (or will charge fees for dealing with live tellers). Most services will be fee-based.

The debit card, which bills a customer's account automatically, will eventually replace the credit card, the study predicts. High interest rates now discourage people from paying immediately when they can take advantage of the float with a credit card, retaining use of their money until their check is returned to their bank for payment. But the study predicts that two-tier pricing -- now used at gasoline pumps -- will take hold in other industries, fostering debit card use.

The study predicts that multipurpose cards -- allowing either debit or credit, or debit cards with a line of credit attached -- will become common. And, within five to seven years, many households will bank at home through a computer, if security and costs can be improved.

Given the growing diversity of banking, much of the study is devoted to how banks can match the right services to the right customers. The report stresses not only that banks should define customers by income bracket and age, but also by spending behavior.