NEW YORK — GMAC LLC is closer to becoming a bank and applying for federal bailout funds after investors holding $10.5 billion in company bonds agreed to better terms of a debt swap.

"The committee has unanimously agreed" to support the debt-swap agreement, said Andrew Rosenberg, a New York lawyer representing the bondholders. Investors had initially shot down a proposed $38 billion debt exchange that would have allowed the home and auto lender to become a bank holding company.

GMAC said the amount of notes covered by the agreement represents a significant portion of the minimum amount of regulatory capital needed to help it become a bank and gain a share of the federal bailout.

However, significant additional participation will also be required, and in order for such condition to be satisfied, the estimated overall participation in the offers would need to be approximately 75 percent on a pro rata basis. The Federal Reserve has informed GMAC that if it is unable to meet these capital requirements, the Fed will not approve GMAC's application to become a bank holding company.

The debt swap deal could also give GMAC access to the Treasury Department’s $700-billion rescue fund and allow it to sell bonds backed by the government. In a filing last month, GMAC said if the exchange isn’t completed by the end of the year there was a significant risk it will default on its debt.

In addition, General Motors Corp. said Monday it would allow GMAC to delay up to $1.5 billion in payments for vehicles shipped to dealers until Dec. 30, which will help maintain liquidity through the end of the month.