NEW YORK – Bank of America reached an $11.6 billion settlement with government mortgage agency Fannie Mae to settle claims resulting from mortgage-backed investments that soured during the housing crash, bringing it a step closer to clearing up its legacy of bad home loans.

Under the deal announced Monday, Bank of America will pay $3.6 billion in cash to Fannie Mae and buy back $6.75 billion in loans that the bank and its Countrywide Financial unit sold to the agency from Jan. 1, 2000, through Dec. 31, 2008. That includes about 30,000 loans.

The bank is also paying $1.3 billion to the agency for failing to deal with foreclosures fast enough.

For Bank of America, the settlement with Fannie Mae over the mortgage investments represents a “significant step” in resolving the bank’s remaining mortgage problems, Bank of America CEO Brian Moynihan said.

The settlement represents “another step closer to normal” for Bank of America, Wells Fargo analyst Matt Burnell wrote in a note to clients. Burnell said the deal is good for the bank because it will likely reduce the provisions it has to set aside to cover claims from investors over faulty mortgages that were sold with incorrect data.

Bank of America’s July 2008 acquisition of Countrywide, when Ken Lewis was the bank’s CEO, was initially praised because the lender was seen as stepping in to support the mortgage industry. Instead of boosting Bank of America’s business, however, the purchase has drawn a drumbeat of regulatory fines, lawsuits and losses.

Fannie Mae and Freddie Mac buy mortgages from banks and repackage them as bonds they sell to investors.

During the housing boom, banks sold loans to the two agencies that should never have been issued, because the banks failed to carry out the necessary diligence before making them. For example, banks sometimes failed to confirm customers’ income.

In September, Bank of America also agreed to pay $2.43 billion to settle a class-action lawsuit related to its takeover of Merrill Lynch, another of Lewis’acquisitions during the financial crisis.

The Charlotte, N.C.-based bank said it would pay for the Fannie Mae settlement in part from existing reserves, though it would record a $2.7 billion hit to its fourth-quarter earnings for 2012 from the settlement, as well as taking a charge of $2.5 billion for the settlement over foreclosure practices.

Despite the charges, Bank of America still expects its earnings for the period to be “modestly positive.” Bank of America is scheduled to report earnings Jan. 17.