GMAC, the General Motors Corporation financing affiliate that received a $6 billion capital infusion from the government, said holders of $21.2bn of debt agreed to swap their stakes for $15.7bn of new securities plus cash.

Completion of the exchange offer will ease the debt burden of GMAC, which last week won Federal Reserve approval to become a bank holding company, enabling it to tap lower-cost funding and easing concern about its survival prospects.

The lender's other major investor is the private equity firm Cerberus Capital Management.

GMAC said it agreed to accept tenders from holders of $17.5bn, or 59 per cent, of old GMAC notes, and $3.7bn, or 39pc, of notes issued by its Residential Capital mortgage unit.

It said holders of the swapped GMAC notes will receive $11.9bn of new senior guaranteed notes and $2.6bn of preferred stock that never matures.

Holders of the swapped ResCap notes will receive $1.17bn of new GMAC notes. Some investors who participated in the exchange offer will receive cash for their holdings, it said.

Detroit-based GMAC is trying to recover after suffering $7.9bn of losses in the 15 months ended September 30. Most of its losses came from ResCap, but credit problems on car loans had also begun to rise.

The Treasury Department earlier agreed to buy $5bn of senior preferred equity in GMAC, using funds from the $700bn Troubled Asset Relief Programme.

The Treasury also agreed to lend GM up to $1bn to support GMAC.