WASHINGTON — GMAC Inc., the auto and home lender bailed out twice by the U.S. government, received a third rescue package valued at $3.8 billion that gives taxpayers a majority stake in the Detroit-based company.

The infusion will bolster lending at GMAC as it absorbs the $3.8 billion in new pretax charges and decides what to do with its loss-plagued home mortgage unit, according to statements from the government and the company yesterday. The aid comes on top of about $13.5 billion previously earmarked for GMAC, which regulators have said is crucial to the U.S. auto industry.

The lender is struggling to return to profitability amid losses at the Residential Capital mortgage unit, known as ResCap, which GMAC may close or sell. GMAC is the primary lender to General Motors Co. and Chrysler Group LLC, automakers that both went into bankruptcy during the recession.

While the Obama administration would prefer not to be involved with GMAC, automakers "are too important for the company to just go under," said Mirko Mikelic, senior portfolio manager at Fifth Third Asset Management, which owns GMAC bonds. "The government also wants to have another option in the housing market, even if ResCap is on life support."

The rescue package calls for the Treasury to buy $2.54 billion of trust preferred securities that pay 8 percent, and $1.25 billion of mandatory con-vertible preferred stock, known as MCP, at 9 percent, according to the statements. The government also received warrants to buy more securities.

The Treasury's current holding of non-convertible preferred stock will be swapped for $5.25 billion of the new MCP, and $3 billion of Treasury's existing MCP will be converted into common, GMAC said.

When that's done, the U.S. stake will rise to 56.3 percent from 35.4 percent. The U.S. also controls General Motors, GMAC's former parent, whose stake shrinks to 6.7 percent. The stake held by Cerberus Capital Management LP, a New York-based investment firm, fell to 14.9 percent from 22 percent. An independent trust for the benefit of GM holds about 9.9 percent, GMAC said. GMAC doesn't have publicly traded shares.

"In May, the Treasury Department made a commitment to all institutions that engaged in the stress tests that we would ensure their capital needs are met," Treasury Department spokes-man Andrew Williams said in an interview. "We are making good on that promise."

The Treasury said the aid is less than originally planned because restructurings at GM and Chrysler caused less disruption at GMAC than regulators expected.

GMAC affirmed that it's looking at "strategic alternatives" for ResCap, ranked among the nation's 10 biggest home lenders and once one of the largest marketers of subprime mortgages. The parent company wrote down $2 billion in ResCap mortgage assets and set up a $500 million reserve tied to the servicing unit that does billing and record-keeping for home loans.

GMAC contributed $2.7 billion of capital to ResCap in the form of mortgage loans acquired from the Ally Bank unit, debt forgiveness and cash, according to the company statement. GMAC "does not expect to incur additional substantial losses from ResCap," the company said.

At the Ally unit, GMAC bought "certain higher-risk mortgage assets" at fair value of $1.4 billion, which triggered an estimated $1.3 billion pretax charge. Those assets were contributed to ResCap. GMAC also gave $1.3 billion of cash to Ally to maintain its capital, the statement said.

"By protecting the financial performance and strength of our core automotive finance operations, we expect to increase the pace at which we can fully repay the U.S. taxpayer," chief executive Michael Carpenter said in a statement.

The infusion is the final dose of capital needed to close a shortfall found by Federal Reserve stress tests in May. GMAC asked the Treasury Department to delay providing the cash when Carpenter was named CEO, replacing Alvaro de Molina on Nov. 16. The deadline for meeting the requirements had been Nov. 9.

The U.S. will also name two more board members in conjunction with its increased stake.