Annuity checks for 100,000 retired federal and military personnel in the Washington area will go up 8.7 percent in April to reflect their adjusted cost of living based on last year's inflation rate.

This is the first cost-of-living adjustment in a year for retirees, whose average monthly benefit before taxes is $958, according to the Office of Personnel Management. Federal workers got a 4.8 percent raise last October.

The 8.7 percent adjustment that will show up in April checks is effective March 1. It will boost the monthly government payout to nearly two million former civil servants or their survivors to $1.6 billion.

Until last year, retired federal workers, postal employes and ex-military personnel got COL raises each March and September. But despite a campaign promise not to tamper with the frequency of U.S. pension adjustments, President Reagan persuaded Congress to drop the September increase.

Federal and military retirement benefits are pegged to the rise in living costs as measured by the consumer price index. Pay increases for civilian workers are based on those in the private sector, subject to shaving by the president with the consent of Congress.

Federal workers last year were due a catchup-with-industry raise in excess of 13 percent. But President Reagan said that the nation could not afford the scheduled increase.

Administration officials are working on a variety of legislative proposals that would cut down future COL raises for government retirees. One of them would be to give retirees raises that reflected either the cost-of-living or the percentage pay increase that federal workers get each year, whichever is lower. Under that formula, retirees this year would have received about half of the raise they actually will get in their April annuity checks.