Interest rates may have peaked today and started down again.

Bankers Trust Co., the nation's eighth-largest bank, cut its prime lending rate from 15 3/4 to 15 1/2 percent. Its move was immediately followed by several other banks across the nation.

The big New York bank cited a decline in the cost of obtaining money as the reason for its action.

Stock prices soared on the Bankers Trust announcement -- the stock market and interest rates tend to move in opposite directions. The Dow Jones industrial average climbed 16.98 points to 828.75. But the Dow remained well below its 1979 peak of 897.61, which it hit Oct. 5, the day before the Federal Reserve Board announced a new tighter-money policy that sent interest rates into orbit.

The Fed's objects have been to cool loan demand and the economy generally, to combat inflation. Though not all economists agreed, today's developments looked like a turning point.

The prime rate applies only to short-term business loans, and goes only to referred customers. Others pay more.

Should today's action signal a revival of the record increase in interest rates that began last summer, it will be some time before consumers, especially home buyrs, feel much effect.

Home buyers have been paying record rates on mortgage loans -- as high as 14 percent. In many cases mortgage money is not available at any price because the major sources of home loans -- savings and loan associations and mutual savings banks -- have been losing deposits.

Because of the record rates obtainable on other investments, such as treasury bills and money market funds, savers have been pulling deposits out of financial institutions.

Many credit unions as well have had to stop making loans because of dwinding deposits.

"Until rates get below 11 percent, and probably not until they get below 10 percent, will savers begin to put their money back into financial institutions," said Richard Everett, chief economist for Chase Manhattan Bank.

Analysts also are not in agreement over whether today's prime rate cut -- which has not been followed by other major banks in New York, Chicago and California -- does indeed represent the long-awaited beginning of a decline "is probably the real thing" temporary lull.

Some analysts such as patrick Savin of Drexel Burnham Lambert said the decline "is probably the real thing." With the economy moving into a recession, he said, demand for credit by both consumers and business will decline. As demand for loans fall, so will interest rates.

Others, such as Leon Gould of Commercial Credit Corp., are worried that continued high inflation, which would be worsened by an expected boost in oil prices next month, heavy credit demands by the federal government and a final burst of consumer spending for Christmas will conspire to keep interest rates high for several months.

He pointed out the prime rate fell briefly several other times this year, only to resume its steady climb to record levels.

In the six weeks since the Fed embarked on its new policy, interest rates have climbed sharply, stock and bond prices have fallen and the dollar has stabilized.

The prime rate, which was at 11 1/2 percent in July, rose steadily to 13 1/2 pecent last October. It then shot up to 15 3/4 percent.

Other short-term interest rates climbed even higher, but have been declining the last three weeks as the markets began to adjust to the new Fed policy.

Until the Oct. 6 announcement, the Fed used to control interest rates on a day-to-day basis.

After Oct. 6, the central bank said it would let interest rates fluctuate freely and instead focused on controlling growth of the money supply -- currency in circulation and checking accounts. The markets panicked and interest rates jumped sharply.

Some, such as the federal funds rates (the interest banks charge each other for overnight loans), reached as high as 18 or 20 percent. The federal funds rate --once the interest rate the Fed tried to control -- traded about 12 1/2 percent today.

Many economists said the sharp jump in rates was an over-reaction to the new Fed policy and added that recent declines represent the adjustment of financial markets to the Federal Reserve.

The Fed's new policy does seen to be having the desired effect. In the last four weeks the money supply has been shrinking at an annual rate of 4.8 percent and business loans have declined sharply -- falling $364 million last week alone.

Most economists believe the growth of the money supply influences how fast prices rise, although there is sharp disagreement among them as to how important a factor the money supply growth is in inflation.