The prime lending rate fell again today as Chemical Bank, the nation's sixth largest, announced it would slash its key business interest rate to 17 percent from 17 1/2 percent.

At the same time, most other short-term interest rates continued to decline in the face of a looser Federal Reserve monetary policy and amid signs that the economy is beginning to slow down.

Long-term interest rates continued to decline as well, helping to push up the prices of both government and corporate bonds. Bernard Harmon, of the brokerage firm Drexel Burnham Lambert Inc., said that bond prices increased on average about $7.50 per $1,000 of face value today, and that during the last week bond prices have risen about $50.

Two major new corporate bond issues -- from American Telephone & Telegraph Corp. and from General Electric Corp. -- have been sold in full to investors, Harmon said, and the AT&T issue is trading at a $10 premium to its face value.

The cut in the prime lending rate, supposedly the interest banks charge their best corporate customers for short-term loans, was not unexpected. Interest rates in the open market, where banks obtain much of the funds they lend to their customers, have been falling faster than the prime rate.

Banks, which lost money late last year and early this year when open market interest rates rose faster than they could increase their prime rates, have been reluctant to cut rates quickly now in order to recoup some profits. But competition from foreign banks as well as sharply lower rates in the commercial paper market (where big companies sell their IOUs to other companies) have forced U.S. banks to trim their rates in order to regain some loans.

Last week Chemical was the first major bank to cut its prime rate from 18 to 17 1/2 percent. By Tuesday, most major banks had matched Chemical's rate. No major bank followed Chemical down to 17 percent today.

However many major banks, including Citibank and Continental Illinois, trimmed the rate they charge brokers for overnight loans to 15.75 percent. Cuts in the broker loan rate are generally a prelude to reductions in the prime lending rate.

The broker loan depends heavily on the price banks themselves have to pay for so-called "overnight" money. The chief source of overnight money is in the federal funds market -- where banks lend excess reserves to each other. The Federal Reserve, the nation's central bank, has a major impact on the federal funds rate through its buying and selling of government securities in the open market.

Federal funds have been trading well below 15 percent for the last few weeks and fell as low as 10 3/8 percent at one point today. Less than a month ago, the federal funds rate was above 16 percent.

The Federal Reserve seems to have eased up on its tight monetary policy in recent weeks because it has slowed the growth of money (checking accounts and currency) in the economy.