Under the plan, federal officials said, about $5 billion would be cash payments to states and federal authorities, $17 billion would be earmarked for homeowner relief, roughly $3 billion would go for refinancing and a final $1 billion would be paid to the Federal Housing Administration. If nine other major mortgage servicers join the pact, a possibility that is now under discussion with the government, the total package could rise to $30 billion.

Because of a complicated formula being used to distribute the money, federal officials say the ultimate benefits provided to homeowners could equal a larger sum — $45 billion in the event all 14 major servicers participate. There are additional incentives for banks to distribute the money in the next 12 months.

More than just an attempt to aid consumers and stabilize the housing market, administration officials cast the settlement as an effort to finally hold banks accountable for their misdeeds, more than three years after the mortgage meltdown brought on a full-scale financial crisis.

The deal announced Thursday is about “righting the wrongs that led to the housing market collapse,” said Eric H. Holder Jr., the attorney general. “With this settlement, we recover precious taxpayer resources, fix a broken system and lay a groundwork for a better future.”

Financial shares were mixed after the announcement, but most analysts said they considered the settlement to be good news because it removed one cloud hanging over the industry, adding that the banks had already set aside most of the money. Bank of America, which will pay the most as the nation’s biggest mortgage servicer, actually rose half a percent to $8.18 a share in late morning trading.

American Families....Under Water

Despite the billions earmarked in the accord, the aid will help a relatively small portion of the millions of borrowers who are delinquent and facing foreclosure. The success could depend in part on how effectively the program is carried out because earlier efforts by Washington aimed at troubled borrowers helped far fewer than had been expected.

Still, the agreement is the broadest effort yet to help borrowers owing more than their houses are worth, with roughly one million expected to have their mortgage debt reduced by lenders or able to refinance their homes at lower rates. Another 750,000 people who lost their homes to foreclosure from January 2008 to the end of 2011 will receive checks for about $2,000. The aid is to be distributed over three years.

The deal grew out of an investigation into mortgage servicing by all 50 state attorneys general that was introduced in the fall of 2010 amid an uproar over revelations that banks evicted people with false or incomplete documentation.”