The last time a new savings and loan association opened in metropolitan Washington, you probably could get a 30-year, fixed-rate mortgage at 8 1/2 percent. Well, perhaps not that long ago, but in the past three years, at least, the demand for new S&L charters has been virtually nonexistent.

In the past year, in fact, mergers and acquisitions rather than expansion have shaped the industry nationwide as regulators and S&L executives sought a recovery from the worst earnings crisis in more than four decades.

Now, however, investors, including many in the Washington region, apparently are convinced that the industry has turned around and that an S&L charter is their passport to huge profits.

Indeed, Andrew S. Carron, author of a new Brookings Institution study, said that "the crisis is over" and the industry's future appears healthy after a near collapse in 1982. Even though further substantial consolidation is expected to reduce the number of firms to 2,500 or fewer from 4,002 in 1980 and 3,433 at the end of 1982, lower interest rates and new government policies have arrested operating losses and erosion of net worth, the Brookings study points out.

Carron forecast a bleak outlook for the thrift industry in another study last year but now believes it has been rescued.

With lower interest rates in effect and the option to use new powers granted by Congress last fall, "There's no reason why an S&L can't be profitable in a new market," said an official at USA Savings and Loan in Rockville.

USA, which opened four weeks ago, is the second Maryland-chartered S&L to open in metropolitan Washington in eight months. Bay State Savings and Loan of Waldorf opened in November. Another group of investors has applied for a state charter to open what is planned as Maximum Savings Association in Potomac.

Interest in starting savings and loan associations has picked up considerably in recent months, according to the Maryland Savings Share Insurance Corp., which insures state-chartered S&Ls. "I think there is a general view by investors that the savings and loan industry has turned around," said Charles C. Hogg, president of MSSIC.

Mark Saurs, president of the Virginia Savings and Loan League, agrees that starting a savings and loan now is probably a wise investment, "...just as it's a good time to start a bank--not because they are identical but because S&Ls now have more latitude."

The biggest factor working in the favor of S&Ls is that they "don't have that excess baggage" in the form of loan portfolios filled with low-yield mortgages in a high interest-rate cycle, Saurs pointed out.

Although he said that he knows of no formal applications pending for new charters, Saurs is keenly aware of the increased interest being shown by prospective investors. And like Hogg, he cautioned S&L officials, particularly those new to the industry, to avoid the pitfalls that resulted in the recent shakeout.

"They should not make any fixed-rate mortgages, and if they make them, they should package them and sell them in the secondary market," he warned. "There should be constant scrutiny of their loan portfolios."

Saurs added: "You'd think a 13 percent mortgage would be gold. Well, we thought 10 percent was gold until it became an underwater loan."

Above all, although the regulatory climate has improved for S&Ls, "they should not get caught in that trap again" by not diversifying their portfolios and by failing to improve management, he said.

Similar warnings are being sounded with greater frequency as the S&L industry, armed with expanded powers, moves quickly down the road to recovery and into a new era of competition.

In a recent address to the Virginia Savings and Loan League, for example, the president of United Virginia Bank underscored the need for a cautious approach by S&Ls in the euphoria accompanying the apparent recovery.

"Attracting deposits and making mortgage money available to your depositors and others is what you do best," said UVB President Douglas H. Ludeman. "It is what comes naturally for you, and you shouldn't forget those roots as you begin to diversify."

Ludeman cautioned S&Ls to diversify wisely and deliberately, and he urged them to "recognize that your diversification is into fields where other competitors have been doing it better than you . . . You must adequately adjust and expand your management capacity to cope with the new services and products."