Interest rates are close to their peak, so analysts believe. Some expect the prime to go up again soon, perhaps tomorrow. But most believe that it will soon start to fall again.

But there is much less certainty about how far and for how long rates will decline.

Some economists now fear that high interest rates could be an enduring feature of this administration, despite official optimism and forecasts of plunging rates. Even Treasury Secretary Donald T. Regan agreed recently, after the prime climbed to over 20 percent, that the rate is unlikely to go below around 15 percent for some time.

President Reagan and David Stockman, director of the Office of Management and Budget, say that once Congress has passed all the spending cuts promised for 1982, markets will respond and interest rates will fall. Alan Greenspan, former economic adviser to President Ford, believes that more vigorous cuts may be needed to persuade markets that inflation really is being fought, particularly cuts in entitlement programs, such as social security, whose growth depends on economic conditions rather than being tied to specific congressional spending targets.

But Greenspan agrees with the view that the major reason for present high interest rates is that the market is gloomy about inflation prospects. A change in "inflationary expectations" would have a big impact on rates, according to this view and, moreover, expectations can be altered by policy changes, even before there is any sign of declining inflation.

Others believe the recent interest-rate run-up is largely a result of sharp credit tightening by the Federal Reserve Board. As the supply of money has been restricted, its price -- the interest rate -- has climbed, they say.

So long as the Fed is trying to keep money growth below the increase in demand for money, they argue, then interest rates will tend to be high. The administration's forecasts for inflation and growth depend on a huge increase in the velocity of money, or the speed with which an individual dollar is turned over, if they are not to conflict with the tight-money policy advocated by Reagan and being pursued by the Federal Reserve Board.

For unless there is a sharp acceleration in velocity, or a flight from holding dollars, there will not be enough money to pay for all the transactions assumed in the official forecast. But as a recent Brookings Institution study pointed out, it is highly unusual for people to cut down on the amount of money that they hold, speeding up its turnover or velocity, without a rise in interest rates.

Brookings' economists went on to say that "the fiscal policy objectives of the Reagn program are clearly on a collision course with the monetary targets," if the projected sharp fall in inflation does not come about. The collision, they believe, would come as interest rates rise to keep money growth on target in face of an expansionary fiscal policy. Rising rates would begin to choke off investment and short-circuit the growth being encouraged by tax cuts.

Congressional Budget Office economists are also skeptical of administration claims that rates will fall sharply this year and continue on down. They have prepared budget estimates using considerably higher figures for the cost of paying interest on government debt next year, and in later years.

The interest rate declines forecast by Reagan are in step with the administration's prediction of sharply slowing inflation. Many forecasters agree that 18 months or so into the Reagan administration, inflation could well be a few important points lower than when he took office. Fewer believe that the drop will continue.

It is certainly true that inflation is a key influence on the level of interest rates. If the value of money is depreciating at, for example, 10 percent a year, then savers will want to receive, and borrowers will be willing to pay, interest rates of at least that much just to compensate for inflation. It is difficult to sustain low rates of interest when inflation is rapid. Conversely, if inflation slows down, then interest rates probably will come down too.

However, inflation is far from the only influence on rates. The balance of fiscal and money policy, the strength of the economy and so of credit demand, and market assessments of how inflation is likely to move, all play a part.

Present interest rates are way in excess of the rate of inflation. As inflation has slipped gently in recent months, interest rates have climbed. Barry Bosworth of Brookings believes that high "real" interest rates -- after allowing for the effects of inflation -- are going to remain throughout Reagan's first term if the president's economic program proceeds.

Reagan's fiscal policy will be expansionary, he says. If the Fed tries to stick to its tight-money targets, which provide for cutting the growth of the money supply in half of 1986, then rates will have to be high in real terms.

Fed chairman Paul Volcker has warned of potential conflict if the budget deficit is not brought down. Publicly and privately he has left little doubt that he would favor a smaller tax cut over the next three years then cuts originlly advocated by the president.

This would ease the Fed's task of controlling the money supply and put more of th anit-inflation burden onto fiscal policy, he believes. Foreign governments whose interest rates are being dragged up by high U.S. rates would also favor a switch, in the hope that U.S. rates would then come down.

Presidential advisers disagree. Although disappointed by the initial Wall Street reaction to the president's program, the White House is saying that a drop in inflationay expectations will bring rates down early this autumn if Congress goes ahead with all the spending cuts agreed to in the first budget resolution.

Greenspan explains his version of inflationary expectations thus: long-term interest rates are now high because the market believes inlfation will continue high. This forces borrowing companies into the short-term market and so pushes up short-term rates. Fed policy has not been the major factor in recent high rates, he says, although many analysts disagree. And once the market sees deep cuts in the spending programs, which have grown most rapidly, then it will cut the "inflationary premium" on long-term rates, he believes.

If market participants truly believed that inflation was about to drop significantly and permanently, then it would make sense for them to lend and borrow long term at much lower interest rtes. But experience suggests that markets want a fairly sizable drop in actual inflation before they bet on lower future inflation.

In addition there are still many on Wall Street who worry primarily about the size of the budget deficit, rather than just about spending. They will only revise their expectations of long-term inflation when they see a shrinking budget deficit. Many experts believe that the administration's deficit projections are over-optimistic. They doubt whether the administration and Congress will succeed in holding spending to the levels forecast, and whether a large tax cut can be compatible with bringing the budget into balance.

In the longer term, analysts mostly agree that interest rates will stay relatively high, in both nominal and real terms. Even Greenspan predicts little change in long-term U.S. government bond rates from now until the end of 1982. He sees a fall from the present 13 to 12 percent rate then, with three-month rates coming down from just over 15 percent to 12 percent.

There is also wide spread agreement that with the Fed concentrating on keeping a tight grip on the money supply, and ignoring the short-term effects on interest rates, there will be many more ups and downs in rates. Financial markets are already much more volatile than they used to be, and many market men expect even sharper and more erratic rate movements in the future.

Before the longer-term pessimism, or administration optimism, can be tested, interest rates are virtually certain to come down -- even if they are destined to go back up again later.

Although recession predictions have been confounded so far this year, most forecasters believe that the economy now is slowing down after the rapid growth of the first three months of the year. As loan demand sips off, the pressure in money markets also could ease and help push rates down.

The latest money supply figures suggest that the Fed has succeeded in choking off the spurt in growth that spurred last month's credit tightening. As the market absorbs this, and the Fed is able to east off somewhat, this could help rates down, too.

But many still will be waiting to see when rates will start on another upward climb.