Most of the nation's major banks cut their prime lending rate yesterday from 9 percent to 8.5 percent, the lowest level in eight years, and expectations that rates will drop further sent the dollar reeling on foreign exchange markets.

The cut in the prime lending rate -- the key rate banks charge for short-term business loans -- followed the Federal Reserve Board's decision Friday to lower its discount rate to 6.5 percent from 7 percent. The discount rate is the cost to financial institutions of borrowing from the Fed.

Economists were divided over whether the latest decline in borrowing costs will stimulate renewed economic growth; some said it is merely another reflection of a weak economy and that rates will have to fall much further before consumers and businesses will start borrowing again.

Foreign-exchange traders clearly believed yesterday that further interest rate cuts were coming and sold dollars to buy other currencies, analysts said.

The dollar fell to a post-World War II low against the Japanese yen, reaching 171.90 yen in Tokyo, and declined against most other major currencies as well.

The dollar has fallen 35 percent against the Japanese currency since February 1985, when it bought 262.55 yen.

A major support of the strong dollar had been the high level of interest rates in the United States. Many foreign investors bought dollars in order to profit from the high rates available here.

The latest reduction in the prime rate was the second in six weeks. Market interest rates -- those that are determined by supply and demand rather than on the basis of administrative decisions by bankers or government regulators -- have been sliding lower for months.

Demand for business loans has been weak at most major banks. Some economists said they believe the underlying economy is much weaker than indicated by the government report last week that the economy expanded at a reasonably healthy 3.2 percent annual rate in the first three months of the year.

The Fed's discount rate reduction was an acknowledgment that short-term rates have fallen, rather than a signal that the government wants further rate reductions, according to William V. Sullivan Jr., vice president and chief money market analyst for the securities firm Dean Witter Reynolds Inc.

While interest rates were falling yesterday, stock prices were rising. The Dow Jones industrial average, the most closely watched barometer of stock prices, rose 15.50 points yesterday to a new high of 1,855.90, surpassing last Thursday's previous record of 1,855.03.

Stock prices generally benefit when interest rates decline because investors seek higher returns than they can get from banks or money market investments such as certificates of deposit or commercial paper. Moreover, when rates decline, investors are more willing to borrow to finance stock purchases.

The reduction in the prime rate was initiated by Chase Manhattan Bank, the nation's third-largest bank. By afternoon, nearly all major banking institutions had followed.

Traditionally, the prime rate has been the interest rate on which most banks base their charges to business borrowers, but it affects consumer borrowing as well. Most consumer loans still are made at fixed rates, but in recent years lines of credit based on the equity consumers have in their homes have been tied to the prime rate. The interest on these loans fluctuates with the prime rate just as it does on business loans.

Allan Sinai, chief economist for the securities firm Shearson, Lehman Brothers Inc., said consumers will benefit most by the decline in interest rates.

He said there is a "perking up of demand," and cited increases in housing activity, consumer spending and net exports, largely the result of the declining dollar. Sinai said lower inflation, lower interest rates, the lower dollar, falling energy prices and the stronger stock market are the seeds of increased economic activity and that "those seeds are beginning to bear some fruit."

But Lawrence Chimerine, of the consulting firm Chase Econometrics, said that the economy is "just plain weak" and that the lower rates are a reflection of low borrowing demand. He said that interest rates will have to fall much further before consumers and businesses will be willing to increase their indebtedness to buy more.

Chimerine said the decline in rates will help business profits because the amount of interest companies will have to pay on their outstanding debts will decline. But he said most businesses and consumers are likely to use their interest savings to pay off some of their debts or build up savings accounts.

Chimerine acknowledged that economists are widely divided on the economic outlook. "There isn't just disagreement about where we're headed. There's confusion about where we are now."