Second National Building & Loan Inc., an Annapolis bank, reported a 20.6 percent increase in nine-month earnings over the same period last year. The company earned $3.1 million ($2.10 a share) in the latest period, up from $2.6 million ($3.09) a year earlier, based on a weighted average of shares outstanding of 1.49 million this year and 856,200 for the first nine months of 1983. Total assets as of Sept. 30 rose to $447.6 million from $271.1 million a year earlier, an increase of 65 percent.

Earnings for the third quarter totaled $1 million. Second National opened new branches in Ocean City and Edgewater, Md., last August. The company has 12 branches throughout Maryland and Delaware, and specializes in resort, commercial and real estate lending.

* Universal Security Instruments Inc. reported earnings of $65,631 (2 cents a share) for its second quarter ended Sept. 30, up 221 percent from profits of $20,417 (1 cent) for the same period of 1983.

Universal, based in Owings Mills, Md., is a designer and manufacturer of telephones and home security devices. The firm said its sales had increased to $3 million in this year's second quarter from $2.5 million last year.

For the first half of the year, however, the company lost $904,200 (24 cents) on revenue of $4.8 million, compared with a loss of $160,999 (6 cents) on sales of $5.2 million the year before.

* Computer Entry Systems Corp. reported third-quarter net income of $439,000 (11 cents a share), up 122 percent from profits of $197,000 (5 cents) the previous year.

The Silver Spring company, which manufactures cash management and payment processing systems, said its sales rose to $7 million this year from $4.7 million last year.

For the first nine months of this year, earnings rose 81 percent to $913,000 (23 cents) from $504,000 (13 cents) the previous year. Sales increased to $18.9 million from $11.8 million in 1983.