American Security Corp., the District's second-largest bank company, reported an 18 percent drop in first-quarter net income to $5.8 million (50 cents) from $7.1 million (63 cents) in the same period last year. The company's earnings, however, improved sharply from the $11.9 million loss ($1.04) it reported in the fourth quarter of 1984.

The bank company's assets rose to $3.87 billion, compared with $3.78 billion at this time last year.

In January, American Security Chairman W. Jarvis Moody resigned and was replaced by Daniel J. Callahan, who was a president of rival Riggs National Bank until he became American Security's president in 1983.

Bank sources attributed Moody's resignation to his health and the pressures he would face in coming years because of the bank company's problem-riddled loan portfolio. American Security's loan losses began to mount last spring.

In December, the bank company announced that it had agreed to make a $37 million addition to its reserves as a cushion against possible loan losses.

The provision for loan losses for the first quarter was $6 million, compared with $4.9 million in 1984's first quarter. Additions to loan loss reserves are subtracted directly from earnings.

Even though the bank is financially stable, analysts have said that it will be some time before it can return to its traditional level of profitability.

Washington Bancorp., parent of the National Bank of Washington, announced a decline in net income of 5.8 percent to $2.36 million ($1.70 per share) for the first quarter of 1985, down from $2.5 million ($1.82) during the same period in 1984.

However, earnings showed a marked improvement over the immediately preceding quarter, the last quarter of 1984, when net income dipped by 89 percent.

Although interest income rose 13 percent and non-interest income rose 43 percent during the first quarter of this year, Washington Bancorp.'s net income was affected by increased loan loss provisions. These were increased by $2.8 million, up from the $825,000 in loan losses a year earlier.

The increased allowance for loan losses, now totaling $14.3 million, reflects the bank's more conservative evaluation of its problem loans.

First Virginia Banks Inc. reported a 2.9 percent net increase in earnings to $8.7 million (60 cents per share) in the first quarter over the same period in 1984.

Last year's first quarter earnings of $8.5 million (59 cents) were restated to reflect the accounts of four banks acquired during the second quarter.

First-quarter net operating income rose 9.9 percent from last year, when it totaled $7.9 million (55 cents). The increase resulted from a tax refund as well as interest income.

Entre' Computer Centers Inc. of Vienna, a franchisor of retail computer stores, realized a 77 percent increase in profits during the quarter ending Feb. 28.

Net earnings amounted to $2.8 million (29 cents per share), compared with $1.6 million (17 cents) the previous year.

Sales reached a record $9.5 million, up 93 percent over the $4.9 million recorded in the same quarter last year.

Entre' President Steven B. Heller said retail sales of computers, related equipment and software reached a record level in December.

The company inaugurated 13 new franchised centers in the quarter, including one in Rotterdam, bringing the number of centers now open to 247 with 40 more under development.