Madison National Bank yesterday announced this area's first home banking service, beginning June 1, which will permit customers to pay bills using small personal computers connected by telephone line to the bank's computer.

To participate in Madison's "Home Teller" service, customers will have to pay a $15 monthly fee and maintain a minimum balance of $2,500 in an interest-free checking account. In return, the bank will provide customers with a Commodore 64 personal computer as well as the other equipment needed to bank by computer over the telephone lines from home.

Customers will need a push-button telephone and a television set, on which the customer's records will be displayed.

Norman Hecht, Madison senior executive vice president, said customers will be limited at first to paying up to seven pre-selected bills a month, although that number will increase.

Hecht said the bank expects to recoup the cost of developing the home banking program within a year to a year and a half. If Madison, which has assets of about $212 million, can sell its program to other banks, it will recover costs sooner, he said.

Hecht declined to reveal how much Madison spent to develop its version of home banking, but said that it is much less than giant banks like New York's Chemical Bank have spent. There are about 30 home banking experiments being conducted around the country.

Madison's program will be one of the first that is a commercial operation rather than an experiment.

To start, Madison will permit up to 2,500 customers in its home banking program, but Hecht said the number will grow as the bank's ability to process the accounts grow.

Madison Chairman Donald K. Menafee said the computer equipment the bank will provide "Home Teller" customers has a retail value of about $1,000, but computer specialists said the equipment could be purchased for about $600. Besides the Commodore computer--one of the most popular personal computers--the bank will provide a device called a modem that connects home computers with the bank computer over the phone. A disk drive and software also will be provided.

Customers also will be able to use the Commodore for other purposes--from playing electronic games to working on taxes. Hecht said that the $15 fee is for the use of the computer and will be reduced after three years.

Hecht said the bank will make most of its money because it will not have to pay interest on the $2,500 checking deposit. A customer could earn about $135 a year on a $2,500 deposit in a NOW account--that pays 5.25 percent interest--and more in high-yielding accounts such as a money market deposit account.

Madison also will lower its costs by doing transactions electronically rather than by check. A check can cost a bank 50 cents or more to process, while paying a bill electronically can cost about 10 to 15 cents.