The Carter administration is preparing to concede officially that the unemployment rate will climb to 8.5 percent by the end of this year but it also assumes the recession will hit bottom by then, to be followed by a slow recovery.

Preliminary figures compiled for the administration's delayed midyear economic forecast July 21 also predict that inflation will slow substantially in coming months, with consumer prices rising 11.9 percent during 1980 and 9.8 percent during 1981.

The new forecast, markedly different from those the White House made public in March and January, is based on a belief by top presidential advisers that the slide in the auto and housing industries has ended.

As late as last March, the administration was predicting that the recession would be relatively mild but would extend until well into next year. The jobless rate was expected to rise to a peak of 7.25 percent early in 1981.

The White House also predicted last March that inflation would be somewhat higher this year, with retail prices jumping 12.8 percent between late 1979 and late 1980, and 9 percent the following year.

However, in part because of the impact of President Carter's March 14 anti-inflation program, the recession has proved to be steeper than Carter predicted, while inflation appears to be coming down more rapidly.

The latest survey by the Labor Department showed the overall unemployment rate at 7.7 percent in June, up sharply from the 6 percent range at the start of the year. Consumer princes, meanwhile, have slowed visibly.

The new White House forecast would place the administration generally in line with the predictions of most private economists, with Carter slightly more optimistic both on unemployment and on inflation.

Chase Econometrics Associates, for example, is predicting a peak jobless rate of 8.7 percent in the fourth quarter of this year and an inflation rate of 13 percent for 1980 and 9.7 percent for 1981.

Some forecasters even are talking about a possible 9 percent jobless rate before the unemployment rate begins to turn down.

The forecast the administration is preparing -- still subject to minor changes, according to key officials -- assumes Congress will enact a $20 billion to $30 billion tax cut, covering individuals and business, for 1981.

Although the details have not been settled, the forecast assumes that the tax reductions are made effective as of next Jan. 1, but that they don't show up in employers' withholding statements until midyear.

The timing disparity often occurs when a tax bill is considered early in the year. Although Senate Democrats have pledged to take up a tax bill by Labor Day, the White House is pushing to postpone it until early 1981.

The administration's new forecast contains these details:

UNEMPLOYMENT: The jobless rate will rise sharply from the current 7.7 percent of the workforce to a peak of around 8.5 percent in the final three months of this year, and then edge down to just below 8 percent by late 1981.

INFLATION: Consumer price increases will slow substantially, rising by 11.9 percent or so between late 1979 and late 1980 and 9.8 percent or so between late 1980 and late 1981. That could mean a 6 to 7 percent annual rate in July and August.

GROWTH: The "real" gross national product, or actual output of the economy adjusted for inflation, will slump about 3 percent this year and rise by between 3 and 4 percent in 1981.

Officials now are expecting this so-called "real" output to plunge at an 8.5 percent annual rate in the second quarter of this year and at a pace about half that in the current quarter.

Administration officials have said privately they are convinced the breathtaking slide in the auto and housing industries has about reached its end right now, and that any "ripple" effect on other industries is apt to be relatively small.

However, that view is not shared by all forecasters. Some analysts still predict the sharp slump in sales earlier this year will prompt businesses to cut orders severely to work off inventories, delaying any vigorous recovery.