The prime lending rate at many of the nation's major banks hit an incredible 20 percent yesterday, with most bankers expecting the rate to continue to rise.

Business borrowing is still strong despite the unprecedented cost of loans, while the price banks themselves are paying for funds to lend still is climbing, too, analysts said.

Meanwhile, Federal Reserve Chairman Paul Volcker told a congressional committee the Fed will make "every reasonable effort" to achieve the midpoint of the range for money supply growth it has targeted for 1980.

Testifying before a Senate finance subcommittee on a bill to increase limits on the public debt, Volcker said the Federal Reserve is holding money growth to the desired levels. The Fed has set no specific targets for 1981 as yet, he added, but the "operative objective" for next year is to continue monetary restraint as part of the overall government effort to combat inflation.

Citing "pressures of the mortgage market," Moon Landrieu, secretary of Housing and Urban Development, raised the FHA-VA interest rate ceiling for home mortgages from 13 percent to 14 percent effective today.

Conventional mortgage interest rates -- those not carrying a government guarantee -- now range from 15 percent to more than 16 percent across the nation.

The higher FHA-VA rate will cost the purchaser of a home with a $50,000 mortgage an additonal $38 a month. However, the higher ceiling may help sellers who have been paying up to 9 points to mortgage lenders when the buyer was using FHA or VA financing. A point equals one percent of the loan, and those buyers by law can pay only one point. Lenders now are charging so many points because the mortgages carry interest rates below market levels.

Landrieu said there was "no alternative but to raise the mortgage ceiling because mortgage credit is not insulated from the upward movement" of other interest rates.

The FHA-VA rate ceiling on mobile-home loans was also boosted from 17 percent to 18 percent. For mobile homes located on their own lots, the ceiling went from 16 1/2 percent to 17 1/2 percent. The ceiling on property improvement loans was raised from 17 percent to 18 percent.

Chemical Bank of New York, the nation's sixth largest bank, led yesterday's march to a higher prime lending rate, the interest banks charge their most creditworthy customers. Bank of America, the largest, quickly followed.

A month ago the prime was 16 3/4 percent. Six months ago it was 13 1/2 percent.It had reached 19 3/4 percent, at a few banks only this Tuesday.

Many corporate borrowers are turning to blanks for the sort of loans to which the prime rate applies because of several factors. Some who otherwise would issue long-term bonds don't wish to do so because they want to avoid being locked into paying very high interest rates for many years to come. Other business borrowers are tapping bank credit lines to help finance inventories as the cost of such stocks is rising rapidly with inflation.

"The demand for bank loans continues to be strong, putting banks under increasing pressure, so you can figure the prime will move upward some more before peaking," an analyst at Merril Lynch & Co. said.

Volcker told the Senate subcommittee that the best thing Congress can do to lower interest rates is "make some progress on the inflation front. Then you can see interest rates come down."

Cutting spending and balancing the budget is the best way to do that, he said. Those actions "would begin to change the psychology of inflation and take pressures off the financial marets" by reducing federal demands for credit, Volcker explained.

Balancing the budget would do much more than reduce the inflation rate by the three-tenths of a percentage point indicated by some econometric models., he continued. "I don't accept that analysis because . . . it can't pick up the dynamics of the economy."

It would produce "an appreciation of the fact that the government is consistently moving to deal with inflation," he declared.

In other matters, Volcker again ruled out a tax cut until the budget is, in fact, balanced, and raised doubts about the wisdom of President Carter's proposal to withhold income tax on interest and dividend payments. The Fed chairman said withholding would cause "great complications across the board . . . Whether this is the right time for this kind of reform . . . is debatable."