President Reagan said yesterday that interest rates "shouldn't be higher than 10 percent" now because of the drop in the inflation rate, and he used anecdotes about Midwestern bankers to show how lower rates can spur economic recovery.

Speaking from the White House in his weekly five-minute radio broadcast, the president also said the pending budget deficit could be almost wiped out if tax cheaters operating in the underground economy paid the $95 billion they owe. And he defended his proposal to give tuition tax credits to parents of students attending private schools.

Reagan said that interest rates are high despite a lower inflation rate "because the money market, having been burned in past recessions by artificial quick fixes, is afraid that inflation will take off again."

But he cited cases in Ohio and Indiana where lowered interest rates spurred new car sales as proof that "not everyone out there in the marketplace is afraid." Auto dealers in the Youngstown-Warren, Ohio, area sold 2,200 cars and trucks in the first 20 days of March after local bankers lowered interest rates to 12.9 percent, he said. In the first three weeks of February they had sold only 344, he said.

Hursel C. Disney, chairman of the First National Bank and Trust of Plainfield, Ind., a small town near Indianapolis, lowered interest rates to make $2 million available for car and truck loans, with similar results, Reagan added. Disney couldn't be reached for comment and it wasn't clear how the president learned of his actions.

Reagan also noted that General Motors, which he did not identify by name, has lowered interest rates at its lending operation to 12.8 percent until May 31.

"You know, there really is something magic about the marketplace when it's free to operate," Reagan said. "As the song says, 'This could be the start of something big.' "

The president has resisted pleas by congressional leaders and some of his staff to back off from his massive tax cuts and defense spending package in the face of spiraling federal deficits. He reminded his listeners yesterday that on July 1 "you'll start paying 10 percent less income tax on what you earn."

Sen. Alan Cranston (D-Calif.), who gave the Democratic Party's formal response to the Reagan talk, said it is the Federal Reserve Board's policy of tight money--"a policy which the president supports--that is primarily responsible for those high interest rates."

Cranston, who is considering a 1984 presidential bid, said the oil glut, bumper farm crops and tight money--not Reaganomics--have lowered the inflation rate. "The harsh reality is that President Ronald Reagan is presiding over the decline of the American republic," Cranston said. "He is not merely presiding over the decline, he is leading it and contributing to it."

In discussing the underground economy, Reagan said he was sure that those who avoid taxes by dealing in cash are "honest people in most of their activities. They just have a double standard where taxes are concerned. They can be the friendly neighborhood fix-it man, a mechanic, craftsman or a member of the professions."

He said: "As we struggle to trim government spending, it's hard not to think of how close that unpaid tax could come to wiping out the deficit." He even paraphrased an old poem with a punchline that would apply to tax cheaters: "I owe it to my country and my fellow citizens to stop being a freeloader."

On tuition tax credits, a proposal that Cranston noted is expected to die without congressional action this year, the president said the public-school lobby had protested that the aid would benefit students attending prep schools. But Reagan said that most of the schools are church-related and the students are from families earning less than $25,000 a year.

"I think they're entitled to some relief since they're supporting two school systems and only using one," Reagan said.