The price of silver plunged below $10 an ounce today, for the first time since the summer of 1979, as high interest rates continued to depress commodity prices.

Silver fell 21 1/2 cents in New York, to $9.895 from $10.115, and the Commodity Exchange settlement price also was $9.895, down from $10.11. Gold, meanwhile, dropped $13.20 on the Comex, closing at $457 an ounce.

"The only real factor in the markets is high interest rates," said David Waite of the big brokerage firm Drexel Burnham Lambert Inc. "Silver has been following gold down."

Waite noted that silver and gold become unattractive investments when interest rates are high because investors can earn 17 percent or 18 percent on many other investments and because borrowing to support a position in a precious metal (which does not yield any income) becomes prohibitively expensive.

Despite the lower prices of silver and gold, there appear to be fewer financial difficulties among investors than in March 1980, when a steep, three-month plunge in silver prices from nearly $50 to $10.80 an ounce caused serious cash problems for the wealthy Hunt brothers. The Hunts' failure to pay margin calls at the big brokerage firm Bache Group Inc. brought the firm to the brink of collapse.

The decline in the prices of precious metals, as well as in other commodities, has been much more gradual than in the early months of 1980 or in the near-collapse of commodities prices during another high-interest-rate seige last November and December, according to William Byers, director of commodities research for the brokerage house Bear, Stearns.

Furthermore, as a result of the collapse of precious metals in 1980, fewer investors are buying gold and silver -- either the metals themselves or futures contracts. "There is not the type of widespread public participation" in the metals markets that leads to margin problems -- essentially demands that investors put up more cash because of losses in their futures contracts -- at brokerage houses," Byers said.

"Some people aren't covering the calls," said one analyst. "But the problem doesn't seem to be widespread. The firms can handle it."

Although analysts say the decline in precious-metals prices is due mostly to high rates, rumors persist that the Hunt brothers have been liquidating some of their other silver holdings to pay off bank loans they obtained in the wake of the March 1980 silver crash.

"They've got to be selling some of it," said a Chicago analyst who asked not to be identified. "But I have no idea how much."