FOR millions of Americans, their banks will soon be as close as their personal computers (PCs) and telephones.
More and more banks, software companies, and regional phone companies are offering plans that allow consumers to bank electronically at home.
''Convenience in banking used to be driving to the local branch of your bank or to an automated teller machine,'' says Frank Pattillo, chief financial officer of Centura Banks Inc., of Rocky Mount, N.C. ''Now the convenience is not driving.''
His small but innovative bank already lets customers see their account balances, transfer funds, and pay bills at home via a screen phone, which visually prompts users and displays figures in much the same way ATMs do.
Pilot marketing projects for screen phones - which can offer many services in addition to banking - have been carried out in Chicago; Grand Junction, Colo.; Wake Forest, N.C.; Ontario; and New Brunswick. NYNEX plans to sell them in the Boston area next year.
''But many people want to look at a larger screen, their PC screen, when doing their banking,'' Mr. Pattillo adds. His bank is among a number that last week announced programs coming this fall that permit home-banking by computer.
Remote banking helps smaller banks compete with larger banks and their many branches. But this kind of banking is ''the wave of the future'' for all banks, says Linda Parker of Portland, Ore.-based US Bancorp, which operates in five western states. She's vice president of the bank's emerging delivery-services department - a name that itself indicates how banking is moving out of buildings and into the electron stream.
On-line banking customers, like John Liu, a dentist in Seattle, say they like the efficiency of the new programs. ''I'm bad at balancing my checkbook,'' he says. Now all he has to do is call the bank from time to time, and its computer downloads data on his accounts and balances them for him in his own computer, which is loaded with Microsoft Corporation's Money program. He can find out which checks have cleared, and he can pay bills by computer. The bank will mail out payments for him as well as arrange electronic payments - of his phone bill, mortgage, and so on.
''It's worth every penny of the $14.95-a-month charge I pay for the program,'' Mr. Lui says. He banks with US Bancorp, which, along with two other banks, helped develop the program with Microsoft. For $7.95 a month, US Bancorp customers can keep track of their balances by computer, but they do not have electronic bill-paying capability.
Microsoft and Intuit Inc. each announced home-banking programs last week - with participating banks already signed on. These include Bank of Boston, Chemical Bank of New York, Marquette of Minneapolis, First Chicago, US Bancorp, and Chase Manhattan of New York. Some banks - Bank of Boston, and Centura, for example - are offering both software companies' competing programs.
Intuit's is the popular personal-finance program Quicken; it is being adapted to handle on-line tasks for release this fall. Intuit's programs for small businesses in the areas of payroll, bookkeeping, and taxes will also be put on-line.
Microsoft's financial program for individuals and small businesses, Microsoft Money, has been in use in some areas since February 1994. An updated, fourth generation Money will be released in the fall. It will run on Microsoft's new operating system Windows 95, due out in August.
Microsoft attempted to acquire Intuit last year, but the Justice Department aborted the deal in May.
Bank of America Corporation of San Francisco and Nationsbank Corp. of Charlotte, N.C., have bought the No. 3 company in financial software, Meca Software of Fairfield, Conn. With Meca's Managing Your Money program, the banks will offer their own remote-banking services.
These programs are ''proprietary'' services, directly linking customers to their banks. In a further step into cyberspace, Wells Fargo & Co. of San Francisco and Security First of Lexington, Ky., offer banking services over the Internet to anyone who dials in. Customers can link up over the network to their bank accounts.
Millions of people are now candidates for remote banking in the home, says Gary Arlen, president of Bethesda, Md.-based Arlen Communications Inc., whose research firm has studied efforts to establish remote banking for 15 years. He and other experts say American homes hold at least 32 million PCs, with some 5 million more added each year. Some 40 percent of the users have modems, Mr. Arlen says, enabling them to hook up for on-line banking. Large numbers of small businesses have or will soon have on-line PC capability.
Many people and small businesses owning modems use financial software, Arlen says. ''Our research, based on 1,600 interviews in the home, shows that financial services are at the top of the preference list for interactive services, right after entertainment.'' Response Analysis of Prince- ton, N.J., assisted in the research.
''A driving force in the trend is the revolution in personal finance. Consumers are more in tune with their money than in the past,'' says Michael Sullivan of Ruder Finn, a public-relations firm in New York.
''Nintendo-nauts and Internet-auts will carry this trend along,'' Arlen predicts. On-line PC users tend to have more accounts and more money than other people, Ms. Parker says.
Bankers want to pick up such customers. As with ATMs, electronic banking allows banks to cut costs by keeping fewer branches and tellers.
For example, Citibank of New York, a pioneer in the field, in May dropped all fees for its extensive direct-banking services, by which customers access their personal accounts through their own PCs and screen phones. Banks now starting programs with Microsoft and Intuit have not said yet what they will charge, but some experts say eventually all banks will pay the cost of the services.