Investors, encouraged by Monday's steep decline in interest rates, sent stock prices soaring yesterday.

The Dow Jones Industrial Average rose 30.72, the fifth largest one-day rise in stock market history. It was the biggest gain since the Dow rose 35.34 points on Nov. 1 1978, the day President Carter announced the first of several programs to fight inflation and rescue the U.S. dollar. That was the largest increase in Dow history.

The Dow average, probably the most widely used barometer of stock market behavior closed at 789.85. It had lost ground in each of the six trading days before yesterday's steep climb. The Dow, which lost 32.42 points in the previous six sessions, still is more than 100 points below its mid-February peak, when the average topped 900 for a day.

While the stock market responded jubilantly to the decline of nearly two percentage points in Treasury bill rates recorded Monday, the bond market was more restrained. Bond prices were mixed in quite trading, with governments rising slightly in price and corporates and municipals either unchanged or up slightly.

Last week, when Chase Manhattan Bank announced a cut in its prime lending rate from 20 percent to 19 3/4 percent, bond prices rose on the average of $45 per $1,000 of face value, a one-day record. Many major banks since have reduced their prime lending rates to 19 1/2 percent.

After several sessions in which trading volume was slow, yesterday's spurt in stock prices came about in heavy buying. Nearly 48 million shares of stock changed hands on the New York Stock Exchange yesterday compared with 27.6 million shares Monday.

Newton Zinder of E. F. Hutton & Co. said the trading was divided about evenly between individual investors and institutions such as pension funds, life insurance companies and mutual funds that generally buy or sell big blocks of stock.

Zinder said that investors also were encouraged by "buy" recommendations sent out by two widely followed analysts: Joseph Granville, who publishes a market letter, and Stanley Berge, who is an analyst for Tucker, Anthony & Co., which mainly advises institutional clients.

Zinder said that although some further gains in the Dow average may be forthcoming during the next few weeks, "The easy ones are behind us."

Yesterday's euphoria should be dimmed soon by the prospects of a severe recession that will eat into corporate profits.

Although both stock and bond prices move in the opposite direction from interest rates -- and the initial impact of a recession usually is to lower both inflation and interest rates -- the adverse impact of a recession on corporate profits normally pushes off a strong stock market recovery for several months after the onset of an economic slowdown.

Many major companies are reporting lower first-quarter profits than a year ago, and many more are predicting earnings decreases in coming months because of rising costs and declining demand for their products.

"It is clear the recession is now upon us," Du Pont Co. Chairman Irving S. Shapiro said Monday after the giant chemical company reported a $4 million earnings slide in the first quarter despite a $600 million increase in sales.

But for the time being, at least, stock prices are looking at interest rates and not profits. The New York Stock Exchange index., a broader measure than the Dow, climbed 2.01 points to 58.74, its second biggest one-day increase ever behind a 2.12-point gain on Nov. 1, 1978.

Of the 1.915 issues traded on the New York Stock Exchange, 1,398 rose in price and 260 declined.

The American Stock Exchange index rose 11.33 points to 245.03 for its second biggest gain, while the National Association of Securities Dealers index of over-the-counter stocks increased 2.63 points to 135.71.

The stock price surge occurred despite a government report that consumer prices increased 1.4 percent in March.