Acacia Mutual Life Co., a Washington-based holding company for a group of life insurance firms, has received permission from the Federal Home Loan Bank Board to operate a savings and loan association in Northern Virginia.

The Bank Board's approval last month of Acacia's application clears the way for the company to organize a new thrift that will be acquired by The Acacia Group, the flagship organization of the holding company.

The new S&L, Acacia Federal Savings and Loan Association, will be capitalized at about $3 million, a holding company official said. The S&L will begin operating in Annandale in early 1985.

Although Acacia Federal probably will operate several branches in Northern Virginia, there are no plans to open additional offices in the first full year of operation, an official said. In any event, "we will branch very carefully" once a decision is made to expand, said Larry Evans, executive vice president and general counsel at Acacia Mutual.

Acacia Mutual's venture into the thrift industry almost certainly will be limited to Northern Virginia. To begin with, S&Ls are prohibited from branching across state lines except in special situations -- usually interstate mergers, which must have Bank Board approval. Secondly, insurance companies are prohibited from owning more than one S&L.

Evans said Acacia chose Annandale because it already is one of the insurance company's major marketing areas. "The marketing studies we made indicate that the Northern Virginia market is a very good market for home mortages and deposits and Annandale appears to be a growing area for that type of business," Evans said.

Evans also said Acacia officials disagree with suggestions that now is not the best time to start an S&L. He said the new S&L will be structured in a manner that will enable it to build a sound mortgage-loan portfolio.