Earnings of federally insured savings institutions jumped substantially in the second quarter, according to a preliminary estimate released by the Federal Home Loan Bank Board. Net income totaled $1.4 billion, double that of the second quarter a year earlier and almost triple that of the first quarter of this year.

For the first half of 1985, net income amounted to $1.9 billion, compared with $1 billion for the first half of last year. Net income during the month of June alone was $900 million.

Bank board Chairman Edwin J. Gray said the data demonstrate that "savings institution profitability is soaring for the industry as a whole." He projected that total 1985 profits will rise to between $4 billion and $7 billion, besting the record of $3.9 billion set in 1978.

Growth in assets for the first six months slowed to 6.3 percent on an annualized basis. That contrasts with a 20.1 percent annual gain for the same period in 1984. Jumbo certificates in excess of $100,000 accounted for just 2 percent of deposit growth, versus 38 percent during the first six months of 1984.

Gray, who has waged a vigorous campaign against rapid growth without adequate capital in an effort to reduce risky investments, said, "It is almost certain that the slowdown in savings institution growth, coupled with the shift away from jumbo certificates of deposit as a major source of growth, helped to bring about the declining cost of funds in the industry in recent months."

The U.S. League of Savings Institutions reported separately that the average cost of funds during June was 9.06 percent, down from 9.81 in January. At the same time, the average yield on mortgage portfolios was 11.30 percent. The difference, or spread, of 2.24 percentage points represents the highest gross margin the thrift industry has enjoyed since 1956.