Morgan Guaranty Trust Co. reduced its prime rate to 20 percent yesterday, a few minutes after the Federal Reserve announced another sizable drop in the money supply in the week ending Dec. 24.

The 20 percent rate is the lowest now being charged by a major bank. Most banks now have moved their primes down to 20 1/2 percent from the record 21 1/2 percent reached last month.

The drop in interest rates over the past few days, coupled with four successive weeks of falls in the money supply, suggests that the Fed now can ease up on its credit-tightening measures. The narrowest measure of the money supply, M1-A, dropped by $2.5 billion to a seasonally adjusted $383.8 billion in the week ending on Christmas Eve.

The slightly wider measure, M1-B, fell by $2.8 billion in the same week to a seasonally adjusted $409.3 billion. M1-A covers cash and checking accounts at commercial banks, while M1-B includes checking accounts at other savings institutions. Money figures for the next few months are expected to be distorted by the introduction of NOW accounts -- a form of interest-bearing checking account -- at banks and savings institutions across the nation.

The recent easing in money should encourage interest rates to fall further as the Fed eases up on its tight policy. But it is most likely that rates now will fall as quickly as they did last spring. Fed Chairman Paul Volcker has said that in retrospect he believes the Fed allowed interest rates to drop too fast in response to decreases in the money supply during the 1980 recession. Last summer the prime dropped to a low of 10 3/4 percent. t

Most experts believe interest rates will have to stay relatively high this year if the Fed's money targets are to

The December drop in the money supply, which is now apparent, suggests that the economy may have softened considerably during the month in response to the sharp runup in the interest rates. Federal Reserve Governor Nancy Teeters, who has voted consistently against tightening credit by raising the Fed's discount rate, yesterday said "the economy is a lot more sensitive to interest rates than previously thought."

In the four weeks to Dec. 24, M1-A grew by an annual rate of only 2.7 percent from three months earlier. On the same measure, M1-B grew at a 4.9 percent annual rate.