The Federal National Mortgage Association yesterday reported a 32 percent jump in third-quarter earnings, attributing the improvement to lower costs, greater income growth and more tax benefits.

Fannie Mae said earnings totaled $66.4 million (80 cents a share) in the three months ended Sept. 30, compared with $50.2 million (68 cents) in the third quarter a year earlier.

Earnings for the first nine months of 1987 totaled $184.8 million ($2.28 a share), a 40 percent gain over earnings of $132 million ($1.78) for the same period in 1986.

Bruce McMillen, chief financial officer, said four factors chiefly accounted for the increase: decreased cost of debt from replacing maturing debt at more favorable rates; fewer liquidations of high yielding mortgages; continued growth in income from guaranty fees resulting from an increase in outstanding mortgage-backed securities, and a decreased tax rate from investments in tax-advantaged assets.

Washington Bancorporation, parent of the National Bank of Washington, reported a 65 percent increase in profits for the third quarter ending Sept. 30.

Earnings were $3.6 million (59 cents), compared with $2.2 million (44 cents) during the same period last year.

For the nine months, the bank holding companies' losses were $5.5 million (89 cents), compared with profits of $5.6 million ($1.12) the previous year.

The loss was attributed to a decision in June to add $12 million to reserves for possible losses on international loans.

Crestar Financial Corp., formerly United Virginia Bankshares, yesterday reported its net income for the third quarter ending Sept. 30 fell 30 percent from the same period last year.

Profits were $15.0 million (51 cents), compared with $21.3 million (75 cents).

Included in the third-quarter results was an $8.1 million nonrecurring charge for severance and retirement benefits, reflecting the elimination of 527 positions during the period.

For the nine months, net income was $44.7 million ($1.52), compared with $63.1 million ($2.21) for the same period last year.