Perpetual American Bank said it recorded record profits for its third quarter. Net income for the three months ended July 31 was $9.2 million ($1.34 a share) compared with earnings of $155,000 for the third quarter last year.

Income for the year to date was $17.7 million ($2.59) compared with a nine-month loss last year of $3.8 million, the company said.

Perpetual, which went public last August, attributed the enormous leap in part to $5.3 million in after-tax gains from the sale of properties in Washington and $1.5 million from the sale of the bank's interest in a commercial real estate building. The company's chairman, Thomas J. Owen, also cited improvements in net interest revenue and other operating revenue.

*Washington Real Estate Investment Trust said profits were up over the second quarter because of rental increases at its residential properties.

Earnings were $2.2 million (28 cents a share) compared with $2.0 million (25 cents) for the same period in 1984. Net income for the first half of the year was $4.4 million (55 cents), up from $4.1 million (50 cents) for the previous year.

The trust, which owns various shopping centers, apartment buildings and office buildings, also announced the beginning of a 50,000-square-foot addition to the Bradlee Shopping Center in Alexandria.

*Red ink continued to spill during the third quarter ended June 30 at B. F. Saul Real Estate Trust, a Washington-based commercial and residential real estate developer.

The company reported a loss of $3.2 million (58 cents a share) compared with $201,000 (3 cents) for the previous year. For the year to date, the company reported a $4.3 million loss compared with a loss of $2.4 million for 1984. The company blamed the continuing losses on increased debt expenses.