Riggs National Bank reported yesterday that consolidated earnings for the first quarter improved slightly over those for the first quarter of 1979 in spite of the higher cost of lending money and a 15 percent increase in operating expenses.

Net income grew one-half percent to $5.434 million ($1.82 a share) from $5.404 million ($1.81) a year earlier.

Assets averaged $2.590 million, 15.9 percent higher than during the same period in 1979. Deposits averaged $2.050 million, up 8.7 percent, and loans averaged $1.355 million, up 19.4 percent.

Riggs is Washington's biggest commercial band and the owner of Central Charge Service, the region's largest independent credit card system.

Metropolitan Federal Savings and Loan Association of Bethesda and its wholly owned subsidiary, MFS Service Corp., reported net earnings for the first quarter of $444.337 (94 cents a share), down 17.6 percent from $539,578 ($1.14) for the same period in 1979.

The association's cost of money, which makes up approximately 86 percent of its total expenses, increased 14.4 percent from $4.054 million to $4.557 million, President Robert J. McCarthy Jr. said.

First American Bank of Maryland reported a 15 percent increase in income before securities transactions for the first quarter $572,640 (58 cents a share) from $499,092 (50 cents) in the same period in 1979.

President G. J. Manderfield said the increase resulted from 9 percent growth in earning assets, an improvement in net interest margins, a 15 percent increase in fee income and limited growth in noninterest operating expenses.

Carl M. Freeman Associates Inc. a residential and commercial development company based in Potomac, reported a 55 percent increase in net earnings during 1979 from $1.4 million ($1 a share) to $2.2 million ($1.55).

Revenues grew 35 percent from $14.41 million to 19.42 million last year. The company didn't release fourth-quarter results.