BankAmerica Corp. this week became the latest bank to waive fees for on-line banking services.

As of Wednesday, customers can use their personal computers to check account balances, transfer funds, and pay bills, using either a modified version of Managing Your Money personal finance software, the America Online computer service, or the World Wide Web.

Previously, BankAmerica offered home banking only through a 15-year-old, proprietary computer service for which it charged $6.95 per month.

Now home banking charges will be waived so long as customers arrange direct deposit of their paychecks into a Versatel ATM account or have the high-end Prima packaged account. BankAmerica is also throwing in free access to its telephone bill payment service, which normally costs $3.95 a month. But it is charging a one-time, $9.95 fee for the Managing Your Money software.

While home banking services can attract profitable customers, BofA may find it hard to drum up interest in Managing Your Money, a much less popular product than Quicken software, said Richard C. Hartnack, retail banking chief at Unionbancal Corp.

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