In another sign of the fast-deepening recession, the Commerce Department reported yesterday that new factory orders for durable goods plummeted 4.2 percent in April, their sharpest decline in nine months.

The April drop, the third in a row, followed declines of 3.9 percent in March and 0.3 percent in February. The figures on durable-goods ordres are watched closely as an indicator of future economic activity.

Meanwhile, interest rates tumbled furether yesterday in response to speculation in the financial community that the Federal Reserve Board has decided to lower its target for the key federal funds rate.

The perception by the markets began after the Fed apparently made no move to block the decline following a meeting on Tuesday of its policymaking Open Market Committee. The funds rate is the interest on overnight loans by banks.

In another development, a new private survey of the naiton's corporate purchasing managers shows more firms cut production in May than at any time since before World War II. Placements of new orders also dropped sharply.

The survey, by the National Association of Purchasing Management Inc., also showed 67 percent of the organization's membership believes the economy will be worse off this year than in 1979. Last November, 35 percent said 1980 would be worse.

Separately, Federal Home Loan Bank Board Chairman Jay Janis said recent declines in short-term interest rates show the anti-inflation program is beginning to have results but predicted housing won't turn up until late 1980 or early 1981.

Janis predicted that starts of single-family housing units should tumble to between 630,000 and 680,000 this year, compared to a robust 1.19 million units begun during 1979.

The figures on durable goods showed a sharp increase in aircraft orders, which often are volatile. Largely because of this, new orders for nondefense capital goods rose 1 percent April, following a rise of 6.7 percent in March. c

However, new orders declined in virtually all other major industries. Actual shipments of durable goods fell 3.3 percent in April, following a 3.8 percent drop in March. The backlog of new orders expanded 0.4 percent.

The continued decline in interest rates showed up in several actions across the naiton: Two large New York banks, Chemical and Morgan Guaranty, lowered their broker loan rates to 14 percent and 14.5 percent, respectively.

And the Merchants National Bank of Indianapolis cut its prime lending rate for most creditworthy corporate customers to 15.5 percent from 16.5 percent. Analysts say an industrywide cut in the price could come soon.