More and more people letting their fingers do the banking

Now there is a way for people who misplace the family checkbook, go on an extended vacation, or forget an important billing date to get their personal bills paid on time anyway.

The personal finance rescue comes in the form of a telephone banking service being offered by 450 financial institutions in the United States. The automated service has been around for more than 10 years, but only recently has it begun to build up a substantial list of users.

''Telephone banking,'' a West Coast banker said, ''is the very logical follow-up to the use of the automated teller machines. Customers have found out in a real hurry that the basic phases of electronic banking are very convenient, fast, accurate, cross-referenced, and readily available outside of normal banking hours. So now we have customers branching out to use kindred electronic services like phone banking.''

This month Security Pacific National Bank announced it will offer new pay-by-phone arrangements to all of its checking account customers beginning in June. This follows a pilot program of Bank of America, which is still in semi-experimental stages in northern California. But First Interstate Bank, on the other hand, has been promoting phone banking in California for well over a year.

Customers who want to pay bills by telephone can either dial or ''touch-tone'' a toll-free number. Dial calls are handled within certain hours by operators. Touch-tone calls are automatically serviced 24 hours, seven days a week, through punched-in codes.

One bank offers a toll-free 800 number to practice on: Punch in your telephone banking account number; enter your security code number; put in your payee number and amount. At this stage, computer ''voices'' repeat the punched-in instructions to avoid mistakes.

As with a regular checking account, customers receive a monthly statement showing each transaction. To avoid confusion when customers balance their checkbooks, it is possible for them to obtain their current account balance as well as the last five checks cleared and the last deposit posted. Transfers under this system can be made by phone between accounts (savings to checking, etc.); and payments can be arranged for up to three months in the future.

Present costs for the pay-by-phone services are moderate. First Interstate charges $1.50 a month plus 15 cents per transaction (a saving over costs of both checks and postage). Security Pacific charges will be a flat $4 for unlimited service. According to industry records, financial institutions across the nation report mixed response so far. Some pay-by-phone lists include as many as 30 percent of the potential users. Others show only nominal groupings. Financial analysts see the telephone banking plan as a forerunner to availability of many more banking services by home-computer users.