Perpetual Federal Savings and Loan Assn., the largest in the District of Columbia, plans to merge with American Federal Savings and Loan Assn., fifth-biggest in Washington, executives of the two announced yesterday.

Boards of directors of the two savings associations have agreed to the merger and now will seek the approval of the Federal Home Loan Bank Board, a process that could take three to nine months.

If the merger is approved, the new financial institution will be called Perpetual-American Federal Savings and Loan Assn. It will have assets of $1.5 billion and 21 offices in the District and Maryland.

The merger plan calls for Thomas J Owen -- chairman, president and chief executive officer of Perpetual -- to become chairman and chief executive of Perpetual-american.

American Federal chairman Richard H. Sinclair would be vice chairman and his son William F. Sinclair, president of American, would become president and chief operating officer of Perpetual-American.

Both Perpetual and American are in strong financial condition, operating profitably, and are not being forced into a merger, Owen and the Sinclairs said yesterday.

Several smaller savings institution have been involved in merger talks recently because they are suffering heavy losses due to current high interest rates and shortages of mortgage funds.

Owen said Perpetual and American Federal began their discussions about two months ago.

He said the officers agreed to merge because the two have "compatible management styles," branch office systems that do not overlap much and complementary specialties.

American has more experience in the secondary mortgage market -- where funds for mortgages are obtained from institutional sources rather thn private savers -- added Owens. He said Perpetual will need to tap the secondary market for funds in order to grow.

Perpetual, said William Sinclair, is strong in computerization, electronic funds transfer, automatic teller machines and other consumer services, all expected to become more important to savings institutions.

"We gain some reserves and get back in the loan business," added Richard Sinclair. Like many S&L's, Amerrican Federal has been able to make few loans lately for lack of money.

Impetus for the merger, Owen insisted, came not from current problems in the thrift industry but from the future of savings associations. Recent changes in federal regulations will make thrift institutions compete directly with banks, giving them power to make consumer loans, offer checking accounts and move into other banking businesses.

The merger will make Perpetual American big enough to successfully compete with the banks, he added.

The merged savings association will be not only the largest in the District but also the biggest based in the Washington area. Two bigger Baltimore savings associations, Loyola Federal and Baltimore Federal recently have moved aggressively into the Maryland suburbs.

With assets of $1.5 billion, Perpitual-American will still be smaller than the major Washington banks. Riggs national Bank has assets of $2.6 billion; American Security Corp., $2.3 billion; and Financial General Bankshares Inc., $2.3 billion.

Because there are many other financial institutions that are bigger than Perpetual-American will be, Owen said he does not expect opposition to the merger from the U.S. Department of Justice's antitrust division.

Justice department lawyers probably will review the competitive impact of the merger, because Perpetual, already the biggest factor in the local mortgage market, would absorb a major competitor.