Bankers Trust Co. of New York, the nation's ninth-largest bank, yesterday cut its prime lending rate from 12 3/4 to 12 1/4 percent, in line with recent declines in short-term market interest rates.

The news prompted a quick rally in the stock market, with the Dow Jones industrials average up 12.26 points, closing at 1202.96.

Financial analysts yesterday appeared uneasy about how the market would digest the $42 billion worth of Treasury securities that will be auctioned over the next few weeks, beginning today with the sale of seven-year notes.

No other major bank immediately followed the lead of Bankers Trust, but analysts said they expect the lower rate to spread soon. Most large banks dropped their rate from 13 to 12 3/4 percent last month, although Wells Fargo Bank in San Francisco went to 12 1/2 percent at that time.

Since then, the Federal Reserve Board has supplied sufficient reserves to the banking system to keep short-term market interest rates moving downward, as a result of the added money available and of the market's perception that the Fed wants rates lower.

"Despite the disparity between banks, interest rates will be lower by the end of the year, with two fundamental factors pulling them down," said David M. Jones, an economist at Aubrey G. Lanston & Co. "Money growth is below Federal Reserve targets, and the economy is cooling substantially.

"The Fed already has eased a notch, and there are expectations it will ease further," Jones said.

Jones believes the split in the prime among banks is the result of uncertainty over Fed policy and over the future cost of funds. "Also, some banks want to maintain the widest profit margins possible to make up for earnings reductions because of nonaccrual loans," he said.

The key federal funds rate -- the interest that banks charge when they lend reserves to each other -- has been below 10 1/2 percent in recent days. The yield on large three-month certificates of deposit, a significant source of funds for banks, is only slightly higher.

At the same time, many corporate borrowers have turned to sources other than banks for needed financing. Some have been replacing short-term bank debt with longer-term bond sales, including several billion dollars worth of new issues sold in the Eurobond market. Others have been turning to the commercial paper market where rates are lower. Nonfinancial corporations increased their issues of commercial paper -- unsecured corporate promissory notes -- by almost $15 billion in the third quarter alone.

Loans have picked up slightly in recent weeks, but Allan Leslie, vice president and economist at Discount Corp. of New York, said that part of the pickup in loans is seasonal.

"The recent slowing of the economy has brought down credit demands, and despite the fact that loans are growing now, they are not anywhere near as strong as one would have anticipated this time of year," Leslie said.

"But bank CD rates have come down along with the fed funds rate, and this undoubtedly is what prompted Bankers' action," he said.

Meanwhile, the slower pace of the economic expansion continued to be confirmed by new statistics. The Commerce Department reported yesterday that business inventories grew 0.8 percent in August as sales fell 0.2 percent. Stocks of goods held by manufacturers, retailers and wholesalers increased by $4.6 billion. Inventories also rose 0.8 percent in July, when sales were down 0.6 percent.

August was the 14th consecutive month of inventory accumulation that began when the recession ended. Most forecasters do not believe the buildup of stocks is large enough to cause a major cutback in production, as occurred during the 1981-82 recession.

Inventories of manufactured goods, including work in progress, rose the most, up 1.3 percent, or $3.5 billion, to $283.5 billion. Retail inventories grew 0.7 percent, or $1.1 billion, to $79.7 billion, the first monthly increase for that category since April, largely the result of a buildup of cars on dealers' lots prior to the brief strike against General Motors, the department said. Wholesale inventories were virtually unchanged, at $126.2 billion.

Robert Ortner, the department's chief economist, said manufacturers and retailers should be worrying about not having enough on their shelves and in their warehouses and not be concerned about too much inventory accumulation. "Consumers are raring to go. Incomes are there. Confidence is near an all-time high," he said. Ortner noted that retail sales went up in September after two previous months of decline, and added, "If production doesn't follow very quickly, the consumer is going to denude the economy's shelves."

But businessmen, who are trying to keep a tight control on costs, such as those associated with carrying unwanted stocks, were quick to adjust their orders and production levels to the somewhat unexpected drop in sales. Ortner acknowledged that industrial production may have declined in September as a result.

The Federal Reserve will release the September figures for production today.

Separately, the Labor Department said that a broad government measure of workplace efficiency in private business advanced at an annual rate of 2.9 percent last year, the steepest gain since 1977.

The department's "multifactor" productivity figure covers not just labor productivity, usually reported as output per hour worked, but also the contribution of capital.