By Jonathan Stempel

NEW YORK (Reuters) - Finance company GMAC posted a $724 million fourth-quarter loss and was downgraded by Moody's Investors Service on Tuesday, after more customers fell behind on payments for their houses, cars and trucks.

The loss compared with a year-earlier $1.02 billion profit, but improved from a $1.6 billion loss in the third quarter.

Results included a $921 million loss at Residential Capital LLC, the mortgage unit's fifth straight quarterly loss. GMAC said it may still sell all or part of ResCap, after reducing riskier lending and announcing 5,000 job cuts.

Earnings also fell 77 percent in auto finance to $137 million, and 91 percent in insurance to $68 million. GMAC is based in Detroit, and ResCap in Minneapolis.

"We've taken painful and appropriate impairments and reserves throughout the year to set things right," Chief Financial Officer Robert Hull said on a conference call. "We know (2008) will be another challenging year for us, and may call for further aggressive tactics."

Results will hurt General Motors Corp (GM.N: Quote, Profile, Research), which owns 49 percent of GMAC and is scheduled to report on Feb 12.

They will also hurt private equity firm Cerberus Capital Management LP [CBS.UL], which led a group that bought 51 percent of GMAC from GM in 2006.

Cerberus also controlled Aegis Mortgage Corp, which went bankrupt in August, and backed away from an April 2007 agreement to buy H&R Block Inc's (HRB.N: Quote, Profile, Research) Option One subprime mortgage unit. It is also losing money at automaker Chrysler LLC, which it bought in August and where former Home Depot Inc (HD.N: Quote, Profile, Research) chief Bob Nardelli is trying to engineer a turnaround.