American Security Corp. yesterday reported second-quarter profits of $7.4 million ($1 a share), up 15.4 percent from the $6.4 million (88 cents) it earned in the second three months of 1982.

Atlantic Research Corp. reported a 48 percent increase in profits. D.C. National Bank also reported sharply higher earnings for the quarter.

American Security Corp.--whose principal asset is American Security Bank, D.C.'s second largest--said that for the first half of the year net income rose 10.2 percent, from $13.7 million ($1.88) to $15.1 million ($2.12). The bank said the increase in earnings was due to a rise in net interest revenues and growth in fee income.

American Security's assets were $3.5 billion on June 30, compared with $3.09 billion on June 30, 1982.

American Security reported that its problem loans increased to $75.7 million on June 30, from $57 million on Dec. 31. American Security is the only Washington bank to report its second-quarter problem loans. Because of the lingering effects of the recession, problem loans are increasing at most banks. Problem loans include loans more than 90 days past due, loans that have been renegotiated and loans a bank is worried about even if payments are current.

The bank said it added $1.5 million to loan loss reserves and charged off $1.6 million in loans in the second quarter. Its loan loss reserves totaled about $22 million on June 30.

Atlantic Research reported net income of $1.68 million (40 cents) up from $1.13 million (33 cents) in its second quarter last year. Quarterly sales of the Alexandria rocket and research firm climbed to $36.4 million from $29.2 million.

For the first half of its fiscal year, Atlantic Research earned $3.2 million (77 cents) on sales of $68.2 million, up from $2.2 million (62 cents) on sales of $54.9 million in the same period a year ago.

D.C. National Bank reported second-quarter profits of $620,491 ($3.07), up 22 percent from the $509,790 ($2.48) net income during the second three months of 1982. For the first six months, earnings were down 6.4 percent to $1.05 million ($5.26) from $1.13 million ($5.42) during the first half of 1982. Its assets were $216 million on June 30, up 34 percent. Profits Rise For American Security Corp.