GMAC, the lending arm of General Motors (GM), was told Monday night that it will receive $5 billion in support from the Treasury Department, with another $1 billion going to assist its transformation into a bank-holding company.

Treasury said it will purchase $5 billion in senior preferred equity with an 8% dividend in GMAC as part of its broader plan to help the automotive industry.

Cerberus Capital Management, a private-equity firm that also owns Chrysler, owns 51% of GMAC.

In addition, Treasury will lend up to $1 billion to GM, which owns the other 49% of GMAC, in order for GM to participate in a rights offering at GMAC to support GMAC’s reorganization as a bank holding company. That’s in addition to the $13.4 billion in assistance already promised to GM on Dec. 19, and Chrysler was promised $4 billion in the same measure.

The $5 billion amount for GMAC has been sent out -- unlike the money that Treasury said would be made available to auto makers GM and Chrysler. The loans to the auto makers were set to close Monday, but Treasury said only that “we’re making good progress” on those.

GMAC is to give warrants to Treasury of 5% of the preferred-stock purchase that will pay a 9% dividend if exercised. It also must comply with the executive-compensation and corporate-governance sections of the law passed by Congress for the financial-industry bailout.

On Dec. 24, the Federal Reserve approved GMAC’s application to become a bank holding company. It was once the wholly owned financial-services arm of GM.

GMAC said in a press release that “the conditions to its previously announced separate private exchange offers and cash tender offers have been satisfied and that GMAC has accepted all of the validly tendered GMAC old notes and ResCap old notes. The GMAC offers and ResCap offers are expected to settle promptly.”

The auto industry has been hit hard by the recession in the U.S. and around the world. GM’s rivals, such as Ford Motor (F), Toyota Motor (TM) and Honda Motor (HMC) have not been immune from precipitous sales declines and a dearth of cash. The credit crisis has only exacerbated the problem, as even willing car buyers have often been unable to get the loans they’d need to buy the vehicles.

“The company intends to act quickly to resume automotive lending to a broader spectrum of  customers to support the availability of credit to consumers and businesses for the purchase of automobiles,” GMAC said in its press release.