Stock prices declined sharply yesterday for the third day in a row as the prospect of rising interest rates scared investors.

The Dow Jones Industrial Average, the most closely watched of the multitude of stock market indicators, ended the day at 1199.22, down 17.13 points from Thursday, bringing its losses for the week to 31.95 points.

Big Board volume rose to 95.24 million shares yesterday, up from 78.41 million Thursday.

Worries about further increases in short-term rates have bothered investors for several weeks. But those fears were heightened this week after Federal Reserve Board Chairman Paul A. Volcker warned Congress of an impending collision of private and federal borrowing requirements that threatens to drive rates up further.

Salomon Brothers' influential chief economist Henry Kaufman poured more fuel on the interest rate embers yesterday when he predicted the key federal funds rate could be expected to rise to nearly 11 percent within the next year. The federal funds rate is the interest banks charge each other for overnight loans of excess reserves and is a rate that the Federal Reserve can control if it desires.

Kaufman, whose predictions are taken seriously by many investors, said the economic recovery coupled with a tighter monetary policy will drive up both short-term rates like the federal funds rate as well as longer-term rates.

After the New York Stock Exchange had closed yesterday afternoon, the Federal Reserve reported that the basic money supply grew $1.4 billion in the week ended July 20 and that for the last 13 weeks it has been growing at an annual rate of 12.7 percent--faster than the Fed wants it to grow. The money supply, essentially cash and checking-type deposits, is thought by most economists to be a key factor in both inflation and economic growth.

If money grows too fast, most economists think, inflation increases. Investors worry that unless money growth slows soon, the Fed will take steps to reduce the growth, which almost always lead to higher rates.

Most interest rates--from those paid on Treasury bills to those paid on long-term bonds--rose yesterday.

Stock prices tend to fall when interest rates rise because investors find interest-bearing investments more attractive than equities. Higher rates also would tend to hurt the recovery as well as most companies that are carrying a large debt burden.

But Marvin Katz, of the brokerage firm Sanford C. Bernstein & Co., cautioned that the stock market always acts erratically in the summer--when many investors are on vacation--and said the declines of recent days should not be exaggerated. "The market went up 30 points a week ago Wednesday for no reason, too," Katz said.

He said, however, that he is beginning to see a continued erosion of confidence among his mainly institutional clients.

On the New York exchange, only 338 stocks closed higher, while 1,265 stocks closed lower. The New York exchange's own index was 94.27, down 1.44 points from Thursday.

On the American Stock Exchange, where 7.13 million shares were traded, the market value index closed at 238.38, down 2.47 points from Thursday. There were 143 stocks that closed higher, while 546 stocks declined in price.

Big, widely owned blue-chip stocks like General Motors, International Business Machines and General Electric led the price decline on the New York Stock Exchange.