When Peggy Bateman wants to do some banking, she just picks up the telephone or stops by her local SupeRx drugstore in Fort Lauderdale, Fla. On her pushbutton phone, she can punch instructions directing a bank computer to pay her bills. At the drugstore, she makes deposits or gets cash using an automatic teller machine. Ms. Bateman, a 25-year-old bartender, hasn’t written a check or been inside a bank for more than a year. “I don’t even remember what bank hours are,” she says.

For the past decade, bankers have been predicting that most Americans would soon adopt banking habits like Peggy Bateman’s, transferring funds with the telephone or a plastic card, abandoning paper checks and avoiding the frustrations of long bank lines. While that electronic wonderland has been slow in coming, it has finally started to arrive, hand in hand with another banking innovation — interest-bearing checking. These changes will, in turn, change the way bank customers pay for bank services. When all is sorted out, electronics may provide not only the most convenient but the cheapest way to do business with a bank.

Few bank customers in other cities have yet the wide variety of electronic choices offered Ms. Bateman and other depositors at the Hollywood (Fla.) Federal Savings & Loan Association, an innovator in electronic banking. But electronic services — especially the cash-dispensing automatic teller machines — are spreading quickly. About 14,000 of these robot tellers are now scattered around outside banks, in supermarkets and in shopping centers —a 40% increase over a year ago.

Banks now are promoting electronic convenience as a lure to new depositors. Commercials introduce friendly banking machines with names (Tillie the Teller in Atlanta, Miss X in Kansas City) and play jingles extolling 24-hour banking (“The Citi never sleeps” for New York’s Citibank). For many customers, freedom from crowded bank lobbies and banker’s hours may well be a more attractive inducement than the promise of a new toaster.

The consumer eager to embrace electronic banking could begin with automatic deposit of his paycheck. About 8,750 companies, 50% more than a year ago, now offer employees this option; workers’ pay is available in their bank accounts on payday without the need to deposit a paycheck and wait for it to clear. The consumer could go on to pay his bills by phone or instruct the bank to deduct from his account automatically regular bills such as mortgage or car payments.

This electronic banking customer also might get a plastic “debit card.” Instead of borrowing, as in charging a purchase with a bank credit card, the customer can use his debit card to withdraw his own funds from his account. By putting it into a slot, then punching a personal code number into a keyboard, the depositor can get cash from an automatic teller machine. With some automatic tellers, the customer also can use his card to check his balance. A few banks have been experimenting with “point of sale” deductions; using a card and a code number, the customer deducts the amount of a purchase directly from his account.

So far, most debit cards are designed for local buying and banking. But depositors are able increasingly to get money from their accounts even when away from home. About 100 banks have issued Visa debit cards that can be used worldwide to make purchases at stores that take Visa credit cards and to get cash from banks within the Visa system. Unlike Visa credit-card advances, against which interest is charged starting on day one, cash obtained with a Visa debit card isn’t subject to interest. And American Express cardholders whose banks agree to the arrangement can use their American Express credit cards as debit cards to buy traveler’s checks from machines at hotels and airports across the country.

The ability to move funds with the speed of an electronic impulse comes at a time when more and more bank customers are going to want to leave money in their checking accounts as long as possible. Depression-era laws long prohibited banks from paying interest on checking accounts. But in recent years Congress has gradually allowed them to do so in New England, New York and New Jersey through negotiable order of withdrawal (NOW) accounts. Authorization for NOW accounts in the rest of the country is expected later this year.

Less than a stamp

Because banks have paid no checking interest in the past, bankers often have rewarded customers for the use of their money by keeping service charges for checks below their true cost. But as banks begin to pay interest on checking accounts, they will charge more for paper checks—either by raising fees or by requiring larger minimum balances for free checking. Sometimes customers also pay fees for each cash withdrawal from a teller machine and for most other electronic transactions. But many banks, to encourage use of their costly electronic equipment, will hold down the fees for electronic services. For instance, customers of Hollywood Federal now pay 10¢ for each bill paid by telephone. Though this could rise slightly, “We hope always to keep the cost of each transaction below the cost of a stamp,” says Henry Vazquez, a senior vice president.

As electronic services and interest-paying checking accounts proliferate, the banking consumer will face new and tricky choices. Here’s advice from banking executives and consultants on coping with some of the puzzlements:

CALCULATING THE COST

Bank customers will have to be alert in order to get the best mix of low fees and the highest possible interest. Bankers predict that per-check fees, now about IO¢ a check, could rise to as much as 30¢. High check charges make free checking even more desirable. But while free checking with a NOW account sounds like the best deal, a high minimum balance and the low NOW interest rate, usually 5%, may make such a combination uneconomic.

Where NOW accounts are already available, they often require minimum balances as high as $2,000. Let’s say that instead of keeping $2,000 in a NOW account, you can get free checking at the same bank by keeping a $500 minimum balance in an account paying no interest. If you then invest the remaining $1,500 in a money-market fund yielding 12% annually, your total interest for a year would be about $90 more than if you had kept the entire sum in a 5% NOW account.

Of course, if banks are allowed to increase interest rates or if money-market rates drop sharply, the results of such comparisons would change. And where telephone bill paying is offered without being tied to a minimum balance, it may be the best choice of all.

FIGURING THE FLOAT

For some, electronic banking will threaten old, comfortable ways of doing personal business. Paying bills by telephone eliminates the “float” that allowed a few days to cover a check when necessary. People used to cutting it close no longer will be able to go to the corner liquor store and cash checks for more than their current balances a day or two before payday. Many stores are installing computer terminals that let clerks know on the spot if a check is good.

If a telephone bill-paying account pays interest, make sure you have the use of your money for as long as possible. Peter Bryan, president of the research firm Payment Systems Inc., suggests quizzing officials to learn exactly when and how deductions are made from pay-by-phone accounts. If all bills are deducted immediately, don’t lose interest by including a bill due at month’s end in your first-of-the-month call. In some programs, you can arrange to make only one call but still have certain bills deducted later in the month when they’re due.

The biggest float loss of all is with direct-deduction debit-card purchases. If you use a credit card instead, you normally would have 30 days or more to pay the bill without interest charges. Direct-deduction transactions have been the least popular item in the cafeteria of electronic services.

FOUL-UPS AND FLIMFLAMS

Errors and delays in crediting payments have been common with fledgling telephone bill-paying systems. But bank executives claim errors are reduced sharply in time. With automatic tellers, one of the greatest problems has been equipment failure. Banks are reducing such problems by installing a new generation of more reliable equipment and by putting two machines instead of one at each location.

The cash machines also offer expanded opportunities for crooks. Bank customers occasionally have been robbed of money just withdrawn from a bank machine at a late hour. And con artists have developed elaborate schemes to learn an individual’s code number and steal his debit card. Bank officials warn against punching your code onto the keyboard when strangers can see the numbers. Memorize that personal code. Don’t write it on the debit card or on another card in your wallet or purse. Don’t choose an obvious code number such as your birth date.

If your debit card is lost or stolen, your protection is less than with credit cards. Your loss can never be more than $50 on a credit card and you are protected against all loss if you notify the bank or credit card company immediately. In most cases, if someone uses a debit card to loot your checking account, you are liable for up to $50 if you notify the bank within two business days of discovering the card is missing. Wait longer and your exposure rises to $500; after 60 days it becomes unlimited. Services that notify credit-card companies when a subscriber’s wallet is lost or stolen will do the same with debit cards.

In dealing with banks or savings and loans, remember that they are especially eager for your money these days. Bankers have been unsettled by the flow of money to money-market funds and other high-yielding investments, and this may give you bargaining power. For instance, the New York-based National Bank of North America offers a reduction of one-quarter of a percentage point in mortgage interest rates if the borrower opens a checking account at the bank and allows automatic monthly deduction of the mortgage payments. On a 25-year, $50,000 mortgage, a drop from 12 1/4% to 12% would save $9.26 every month. That adds up to $2,778, if the mortgage runs its full life.

A break at the bank

Given the price of gasoline, it’s not surprising that at least one institution — Bank One of Columbus, Ohio — is installing automatic tellers in gas stations. For John Fisher, a senior vice president of the bank’s holding company, therein lies an apt comparison. “Gas stations give customers a price break for serving themselves,” says Fisher. “That’s what we’ll be seeing in the cost of electronic banking services.” The cost of banking, like that of gasoline, is likely to go up, but thanks to the new gadgets and services, the pace should lag behind OPEC’s.