Profits at the nation's savings institutions soared to a record $1.76 billion in the first quarter, but a troubling core of about 75 money-losing institutions remains, the government reports.

Earnings by 1,802 private-sector S&Ls - those that have not failed and been seized by the government - were up 14 percent from the same period a year ago, the Office of Thrift Supervision said.It was the ninth consecutive profitable quarter and the best three-month showing since 1984,when the government began collecting profit and loss data quarterly.

Jonathan L. Fiechter, acting director of the office, attributed the performance to the continuing wide spread between interest rates S&Ls pay on deposits and liabilities and the rates they earn on mortgages and investments.

Also, the level of troubled loans and other assets dropped to $117 billion from $127 billion at the end of December and $202 billion a year ago.

The S&L industry's lobby group, the Savings & Community Bankers of America, proclaimed, "The industry's return to capital strength and stability is undeniable."

Failures have slowed to a trickle. There were only three during the January-March period, compared with 59 for all of last year and 146 for all of 1991.

However, one in 10 S&Ls - 183 - remained on the agency's list of problem institutions, and Fiechter said roughly 75 of those were not earning profits on their basic business of taking deposits and lending to borrowers.

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