Fannie Mae made a commitment three years ago to deliver $1 trillion of financing by yearend 2000 to mostly lower-income groups underserved by the mortgage industry.

On Friday the company said optimistically that it was "on course" to meet the commitment.

James A. Johnson, chairman of Fannie Mae, said it had financed $114 billion of mortgages for 1.5 million families most in need during 1996. The total for the first three years of the seven-year program is $311 billion to 4.2 million families, Mr. Johnson said.

That means Fannie, formally the Federal National Mortgage Association, will have to finance an average of about $172 billion a year for the targeted groups over the next four years. Fannie Mae's total fundings last year were about $175 billion.

"It will continue to be a stretch, but we are on course to reach both the $1 trillion goal and the 10 million-household goal by the end of the year 2000," Mr. Johnson said. The company has not announced interim targets.

The stretch will be made harder by the mortgage market this year. Fannie Mae's internal projections are for a decline in industrywide originations of about 9% this year, to $721 billion. Another year like 1996 would give Fannie about $425 billion toward its $1 trillion goal and leave it with almost $200 billion a year to go.

"We haven't backed off our goals at all," said David Jeffers, a Fannie spokesman. "We've always said a lot of the volume would come in the later years."

The $1 trillion commitment has been met with skepticism in some mortgage circles, but Mr. Johnson has steadfastly defended the program, saying it was a necessary step to galvanize his staff into the kind of action he thought necessary.

Indeed, Mr. Johnson said Friday he was "enormously proud" of what his company had achieved so far. He pointed to these accomplishments:

Of Fannie's total single-family business, 19% was with first-time homebuyers, up from 9% in 1993.

Twenty-five Fannie Mae partnership offices were open as of last year, and three will be added this year.

A $50 million increase in new investments was made with Community Development Financial Institutions.

A commitment was made to invest in "critical" community development projects in 10 U.S. cities through its American Communities Fund.

New investments totaling $250 million were added to its portfolio for low-income housing tax credits.

The groups targeted by Fannie Mae include households with low and moderate incomes, minorities, new immigrants, residents of central cities and other underserved areas, and those with special housing needs.

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