Federal National Mortgage Association directors slashed the Washington corporation's quarterly dividend rate in half early yesterday, setting off a wave of selling by investors who unloaded an unprecedented 2.86 million shares of FNMA by the close of New York Stock Exchange trading.

Stock of FNMA fell $2.37 1/2 to $12 in Big Board trading, with large blocks of institutional holdings accounting for much of the volume. Analysts said the short-term outlook for rising interest rates indicates that the company may find it difficult to operate profitably in the current quarter. t

In later trading on the Pacific Stock Exchange, Fannie Mae dipped another 37 1/2 cents a share to $11.62 1/2, a new low for the stock in the past year.

A payout of 16 cents a share, down from 32 cents in the previous quarter, will be made on Dec. 25 to owners of record Dec. 1. It is the first time that the company had reduced its dividend payment rate and comes at a time when interest rates are approaching the record levels of last spring.

Fannie Mae, which is the nation's largest single purchaser of residential mortages, is suffering its worst year since being transformed from a government agency to a private enterprise 12 years ago. In the second quarter of 1980, Fannie Mae reported a net loss of $16.5 million, which some analysts said placed future dividends in jeopardy.

In the third quarter, however, Fannie Mae rebounded and reported profits of $5.9 million (10 cents a share). Although those earnings were off 90 percent from the 1979 period, interest rates had eased during early weeks of the third quarter and economists generally did not anticipate the sharp runup in rates now taking place.

Battered by the soaring costs of borrowing money to buy mortages, Fannie Mae has paid interest as high as 17.4 percent this year on short-term notes (March) and 15.3 percent for longer-term debentures (April). On Oct. 10, Fannie Mae sold $500 million of debentures with an interest rate of 12 1/4 percent.

In contrast, Fannie Mae's $56.2 billion portfolio of mortages had a net yield in October of 9.14 percent. The company normally makes a profit from service fees and the difference between the cost of borrowing money to buy mortages and the yield on its mortage portfolio. FNMA operations generally aid the housing industry by making more funds available for mortgages.