The global economy, which posted a 5 percent real rate of growth last year, its best showing since 1976, likely will slow to a 3 percent growth rate this year and next, the International Monetary Fund said yesterday.

The IMF also issued an optimistic appraisal of Third World problems, citing the decline in the combined current account deficits of developing countries from $113 billion as recently as 1981 to only $38 billion last year.

Nonetheless, in its "World Economic Outlook," which serves as a convenient analytical backdrop for the Bonn economic summit that starts Thursday, the IMF warned that if the summit countries follow "worse policies" than they now promise, the agency's modestly hopeful scenario could deteriorate into "a significant recession."

Thus, a worst-case scenario could drop the global growth rate to 2 percent in 1985-86, instead of the still-acceptable 3 percent, while an anticipated gentle, 5 percent annual slide in the exchange rate of the dollar could accelerate into a depreciation of close to 20 percent in 1987. In such circumstances, there would be a sharp decline in economic activity in the United States, accompanied by higher interest rates, and with unemployment here rising over 9 percent by 1989.

The consequences of this gloomier perspective would be felt seriously in the Third World, where economic growth could be cut from a projected 4 percent rate in 1985 (up from 3 3/4 percent in 1984) to no more than 1.5 percent.

To avert this, the IMF staff report calls on the United States and other nations running large budget deficits to cut them sharply. It also makes a strong plea for Europe to change labor market and business practices that contribute to high unemployment, and for the abandonment of worldwide protectionist measures.

The report says that the projected decline in the global economic growth rate from 5 to 3 percent in its "baseline" scenario would represent a better global balance than in 1984, in that it will result from a slowdown in the U.S. pace while demand stays steady or expands in Europe, Japan and the developing countries.

"Thus, for the first time in several years, the economies of each major [developing] region and group of countries are projected to grow at least as fast as their populations," the report said.

The key assumptions of the IMF's "baseline" forecast for 3 percent global growth in 1985-86 were that the Reagan administration would succeed at least partially in its effort to trim the budget deficit; that the major industrial nations will not return to an inflationary monetary policy; that oil prices will remain stable; and, for the sake of "convenience," that the dollar will dip only about 5 percent in real terms against all major currencies, except the Canadian dollar.

The report focused considerable attention on a significant policy failure in Europe that has resulted in an unemployment rate more than twice the rate of five years ago. A similar policy failure, the report said, relates to the American government's inability to control its internal and external deficits and "the high and variable" real rates of interest that have prevailed since 1981.

However, although the report laid blame on resistance to change in Europe that has slowed technological advances on the one hand, and kept real wages too high on the other, it said it "would be a mistake" to try to "force the pace of expansion" in Europe or Japan.