The Federal Reserve Board has agreed to permit the Banca March of Spain to buy a 15 percent interest in Bank of Virginia, the Commonwealth's fourth largest bank, for $20 million, Bank of Virginia Chairman Frederick Deane Jr. announced yesterday.

Banca March will acquire 784,000 new shares of Bank of Virginia stock, for $25.50 a share, in a transaction that will be completed in a few days, Deane said at a meeting with securities analysts in New York.

Juan March, 39, chairman of Banca March, will join Bank of Virginia's board of directors when the transaction is completed.

The March family owns Banca March and has investments in other Spanish businesses, including cement, construction, utilities and real estate. s

The Spanish bank's interest in acquiring a major block of Bank of Virginia stock was announced several months ago, and Deane provided the final details of the transaction yesterday.

The Federal Reserve Board, which can block investment in American banks by foreigners, decided last week that it had no objection to the Banca March-Bank of Virginia transaction, a Fed spokesman said.

The Virginia Commissioner of Financial Institutions and Spanish banking regulators approved the deal earlier, Deane said.

As part of the agreement that put Juan March on the Bank of Virginia board, the March group agreed not to acquire additional stock in the bank.

Banca March's 15 percent interest in Bank of Virginia makes it the largest single stockholder. According to the bank's public records, Delaware Investment Advisors of Philadelphia, which owns almost 6 percent of the stock, is the only stockholder with more than a 5 percent interest.

Deane told bank analysts the Spanish investment will give Bank of Virginia additional capital that will allow it to expand more rapidly.

The $20 million in new cash, he said, "places us in a position to compete aggressively in our marketplace without capital restraints on our ability to grow."

Deane said the bank will use part of the $20 million to redeem an outstanding issue of common stock and will use much of the remainder to repay borrowings.