The latest innovation in banking, the "sweep" account, combining an interest bearing checking account with a money market fund, is headed this way.

The concept was pioneered several years ago by Merrill Lynch for its affluent customers and offered by other money market funds and bank trust accounts as well. In recent months, however, several hundred banks and a few savings and loans from San Diego, Calif., to Bridgeport, Conn., have begun offering the accounts to individuals with a few thousand dollars in their accounts.

In a "sweep" account, customers must usually meet a minimum deposit requirement. Each account is automatically tallied or "swept" by computer each night and any funds above the minimum threshold amount are transferred into the money market account, which pays more than twice the interest rate of the checking account. If a customer's balance falls below the threshold amount, funds are removed from the money market account and redeposited in the checking account.

The Mid-America Bankers Service Company, a corporation representing 6,700 banks in 13 states, has contracted with the Fidelity Fund in Boston to set up a special money market fund for its members. Fidelity projects the banks' fund will have $1 billion to $5 billion in assets in a year. A dozen banks in Oklahoma have initiated a pilot program. MasterCard recently announced formation of a money market fund for banks that sell its credit and debit cards.

In this area, the Bank of Virginia is reliably reported to be ready to sign a contract with the Dreyfus Fund, based in New York. Three savings and loans in Richmond have begun offering sweep accounts. And Washington-based money market funds report considerable interest on the part of banks and savings and loans.

United Savings and Loan Association of Vienna was among the first here to start a sweep account in conjunction with the Fund for Government Investors. To participate in Checkpower, a customer must deposit a minimum of $1,500 in an interest bearing checking (or NOW) account paying 5.25 percent interest. If the balance rises to $2,000, funds are automatically transferred in increments of $500 to the money market fund, which is currently paying 13.4 percent. If the account goes below $1,000, funds are transferred back into the checking account in the same increments to cover the checks. United charges a one-time initiation fee of $25.

Elsewhere, the threshold balance varies between $1,000 and $5,000. Funds move back and forth between the checking and money market accounts in blocks ranging from $100 to $1,000. Some institutions charge a monthly or annual fee.

For consumers, sweep accounts through banks present a number of advantages over direct investments in money market funds. The most obvious is the time factor; investments are made automatically, without the customer having to remember to write and mail a check to a money market fund. Experts say the increased interest earned usually more than offsets the charges paid. Moreover, checks of any amount can be written on the sweep account, not just the $500 plus transactions money market funds permit.

The most obvious disadvantage of the sweep account is the minimum balance. Consumers accustomed to keeping just enough in their checking accounts to cover their checks while stashing all spare cash in a money market fund may not benefit.

For years, banks and savings and loans have been railing at the money market funds, which have been draining off their deposits. Now, as characterized by the adage, "If you can't lick 'em, join 'em," banks are contracting with existing money market funds or having them create special ones in a desperate effort to keep their customers until financial regulators permit them to pay competitive rates or set up their own money market funds.

Not all depository institutions are swept up in the tide. In fact, the vast majority would probably prefer that the whole question be swept under the rug. Bankers admit candidly that sweep accounts are marginally profitable at best and, at worst, a disastrous drain on deposits. As one banker put it, "We're only making money at it because we're the first on the block to offer sweep accounts."