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“Mortgage rates dropped a lot in a matter of a day, which is just what the Fed wanted,” said Patrick Newport, an economist at IHS Global Insight who specializes in housing. “However, it will only affect mortgages eligible to be purchased by Fannie and Freddie,” Mr. Newport said. Although that is a huge market, it likely will exclude many of those who need the most help to avoid foreclosure.

For example, subprime loans and many exotic mortgages, which required the homeowner to pay interest only for several years, will not be affected by the Fed’s initiative, Mr. Newport said.

Jumbo loans that are too big for Fannie and Freddie to buy (more than $730,000 for now, and more than $625,000 beginning Jan. 1) will continue to command interest rates in the neighborhood of 8 percent, analysts said.

The interest-rate decline also will be of no benefit to millions of troubled homeowners who want to refinance their mortgages in states that have been hammered by the bursting of the housing bubble, including California, Florida, Arizona and Nevada, where housing prices have plunged by 30 percent to 40 percent in many markets.

Adjustable-rate mortgages requiring little or no down payments were wildly popular during 2005 and 2006 in the bubble states, and many homeowners in these states are now “under water,” owing more on the mortgages than their houses are worth.

About 12 million U.S. homeowners are in that situation, said Mark Zandi of Moody’s That’s a big increase compared with the 6.6 million homeowners who owed more than their houses were worth at the end of last year. Only about 3 million homeowners were under water at the end of 2006, Mr. Zandi said.