The Dow Jones industrial average plunged 95 points and a key interest rate surged past 10 percent yesterday after the government issued a disappointing report on the nation's trade performance in August.

The financial markets were sent reeling by a Commerce Department announcement that the August trade deficit narrowed by only $800 million, to $15.7 billion, from July's record of $16.5 billion. Many economists had expected a greater decline, to between $14 billion and $15.5 billion.

Stock and bond prices and the dollar all fell sharply as the markets interpreted the report as meaning that the dollar would have to decline further to bring the trade deficit down.

As the dollar moves lower, interest rates must rise to continue to attract foreign investment. Higher interest rates in turn raise fears of rapid inflation and drive investors out of the stock market.

The Dow Jones industrial average, the most widely watched stock market barometer, dropped a record 95.46 points to close at 2412.70. The Dow, which fell 91.55 points on Oct. 6, is now about 310 points, or 11 percent, below the peak of 2722.42 set in late August, and some Wall Street analysts said that the five-year-old bull market is over.

In the bond market, where falling prices cause yields to rise, the Treasury's 30-year bellwether issue fell 2 7/32 points, raising the yield to purchasers to 10.14 percent -- the first time it has exceeded 10 percent since November 1985.

Meanwhile, the dollar fell against other major currencies in foreign exchange trading. {Details on Page F1.}

Further discouraging economists and the financial markets was the fact that the August trade deficit, though smaller than July's, was still the third highest on record, and came with an $800 million decline in exports.

Moreover, the trade figures for the first eight months of the year indicate that the 1987 deficit will be even higher than last year's $156.1 billion level instead of receding, as Reagan administration officials had predicted.

Last spring Treasury Secretary James A. Baker III forecast a $15 billion to $20 billion improvement in the trade deficit this year, but after two months of decline the defict began climbing again in May.

Administration officials were more cautious yesterday, but put the best face on the matter by citing improvements in "the real trade balance," an increase in the volume of exports as measured by dollars adjusted to reflect a constant value and seasonal changes.

But congressional Democrats, pressing for presidential approval of tough trade legislation, attacked Reagan administration trade policies. "In a year when the trade deficit is supposed to be declining, it is $1.7 billion higher than the deficit of August a year ago," said Senate Finance Committee Chairman Lloyd Bentsen (D-Tex.).

"When it comes to trade deficits, America is in a class by itself," added Senate Majority Leader Robert C. Byrd (D-W.Va.).

"The trade figures are still bloody bad," said Stephen Dakin, foreign exchange trading manager in New York for Union Bank of Switzerland. "Where does it all stop? They {administration officials} keep saying they are going to get better, but they haven't yet."

David D. Hale, first vice president and chief economist for Kemper Financial Services in Chicago, added, "Wall Street is beginning to face the fact that the American trade deficit may not come down without a recession."

He suggested a further fall in the value of the dollar to about 130 Japanese yen over the next 12 to 18 months. "They {currency traders} recognize it has to go lower," Hale said.

"For the bond and stock market, you have a day of disaster," said Allen Sinai, chief economist for Shearson Lehman Bros. Inc., who had predicted a trade deficit of $15.5 billion, close to the actual figure.

Sinai said the markets fell because of "not irrational fears" that the continued high trade and budget deficits present "a downside risk for the dollar" that could lead to higher interest rates and greater inflation.

"No matter how you cut it," Sinai said, "there is still not a clearly definable trend of improvement in merchandise trade. The big-picture view is we still have this trade deficit. There is not a significant trend toward improvement yet."

But Jerry Jasinowski, chief economist of the National Association of Manufacturers, said the trade figures "are a bit better than the market is showing," reflecting "the way financial markets and the industrial economy have become decoupled and are moving on somewhat different paths."

Both Jasinowski and Sinai agreed that there are positive elements in the August trade figures that were ignored by the financial markets.

Jasinowski, for instance, pointed to reports from NAM members showing that the manufacturing sector of the economy is rebounding from a deep slump, and noted that improvements in exports are spurring a modest firming of growth. He said there has been a $30 billion improvement over the past nine months in real net exports, which has improved the nation's economic growth.

He added, though, that U.S. manufacturers "are just going to have to be more aggressive" in international markets if they want to win sales.

Without a $600 million decline in overseas sales by U.S. aircraft makers, he said there would have been a $400 million improvement in manufacturing exports in August.

Sinai also pointed to "encouraging aspects" in the August numbers, including a $1.4 billion drop in imports of manufactured products and a lessening of the deficit with all but three major trading partners -- Canada, from $645 million in July to $939 million in August; Brazil, from $87 million to $526 million, and Venezuela, from $207 million to $272 million.

The $4.9 billion deficit with Japan, down from $5.1 billion in July, remained the United States' largest.