J.P. Morgan Chase & Co. is about one-fifth of the way finished with doling out the $4 billion in consumer aid that was required as part of its mortgage-securities settlement with the Justice Department last year, according to a new report the bank submitted to an independent monitor.

The bank calculates it should receive about $869 million worth of credit for actions like slashing mortgage debts for struggling homeowners and lending to low-income home buyers, according to a report released Wednesday by Joseph Smith, who was hired to ensure the nation's largest bank by assets followed the consumer-relief terms as part of its $13 billion Justice Department settlement.

The Justice Department is requiring J.P. Morgan, as well as Bank of America Corp. and Citigroup Inc., to spend money assisting struggling borrowers as a condition of their recent, multibillion-dollar settlements where the banks settled accusations that they had misled investors about the quality of the mortgage securities they sold in the run-up to the financial crisis.

Mr. Smith, a former North Carolina banks commissioner who also made sure that big banks lived up to their consumer-aid requirements after the 2012 national mortgage settlement, said his office still needs to validate J.P. Morgan's calculations before the bank can get credit. J.P. Morgan is paying for Mr. Smith's review, but both the bank and Justice Department had to agree to the hiring.

"We are pleased to have provided more than 46,000 families $7.6 billion in mortgage relief," either through mortgage modifications or loans to struggling borrowers, a bank spokesman said in a statement, adding that the relief adds up to $869 million in credit to the bank, under its calculations. "We are working very hard to help as many homeowners as quickly as possible, and look forward to formal validation of our effort" by Mr. Smith later this year.

According to the report that J.P. Morgan submitted last month to Mr. Smith's office, the bank has so far modified mortgages for nearly 7,000 homeowners. About 2,600 of those borrowers saw their average monthly payments slashed by $540, or nearly 40%, J.P. Morgan calculates.

J.P. Morgan also estimates that it has made mortgage loans to nearly 39,500 struggling borrowers. The bank can get credit toward its $4 billion obligation by lending to borrowers who might otherwise be overlooked, such as low-income first-time home buyers, people who have lost previous homes to foreclosure and short sales, and people in certain FEMA-designated disaster zones.

The bank gets various amounts of credit for different actions. For example, under certain circumstances it can get $1 credit for forgiving $1 in mortgage principal, but it can get more credit for lending in areas that the government deems particularly distressed. The bank receives less credit for modifying loans owned by other investors.

Under the settlement, J.P. Morgan is required to make quarterly reports to Mr. Smith on the progress of its loan-relief activities. His staff is charged with reviewing samples of the bank's cases in detail to validate whether J.P. Morgan has satisfied its obligations.

In late July, Mr. Smith's office released its first report on an initial sample of 100 mortgages that J.P. Morgan modified and submitted for $6.3 million in credit. Mr. Smith's office said at the time that the bank had followed the proper procedures for modifying those loans and calculating the credit it deserved.

Citigroup's $7 billion mortgage-securities settlement in July included $2.5 billion in consumer aid, and Bank of America's $16.65 billion settlement in August included $7 billion for consumer aid. They will also be overseen by independent monitors.

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