Spurred by solid across-the-board performance from operations, a lower corporate tax rate and lower interest expenses, The Washington Post Co. yesterday reported that second-quarter net income increased 39.3 percent over last year.

The company reported second-quarter revenue and net income of $339.1 million and $42.4 million ($3.29 a share), compared with $313.3 million and $30.4 million ($2.37) in the corresponding period last year. For the first half of 1987, the Post reported revenue of $637.5 million and net income of $61 million ($4.74), compared with revenue of $590 million and net income of $42.8 million ($3.33) last year.

Washington Post stock jumped $8 a share yesterday on the American Stock Exchange, closing at $215.

Newspaper division revenue rose 9 percent in the second quarter and in the first half of the year. Washington Post newspaper advertising increased slightly in the first half of the year, from 2,661,400 inches to 2,770,400 inches.

Newsweek revenue increased 1 percent in the second quarter and was even in the first half compared with last year. Domestic magazine advertising increased from 1,185 pages last year to 1,243 pages in the first six months of 1987.

Post-Newsweek television stations' revenue rose 8 percent in the second quarter and 7 percent in the first half of the year. The company's cable television division reported a 15 percent increase in second quarter revenue and a 16 percent rise in the first six months.

Revenue from other businesses, including Stanley H. Kaplan Educational Centers, Legi-Slate and Florida cellular telephone operations, increased 42 percent in the second quarter and 40 percent in the first six months of 1987. The Post Co.'s share in earnings of affiliated businesses, including newsprint operations, rose from $4.7 million in the first half of last year to $6.9 million this year.

During 1986 and 1987, The Post Co. has retired about $100 million in debt. The debt was related to the acquisition of cable television operations in January 1986. The reduction in debt, and a decline in interest rates, helped the company cut interest expenses in half, from $18.8 million in the first six months of last year to $9.1 million this year.

As previously reported, The Post Co. has agreed to sell its Florida cellular telephone operations to McCaw Communications for a price in excess of $200 million. The sale of the Florida properties, which ends the company's involvement in the cellular telephone business, is expected to produce an after-tax gain of about $110 million.