GMAC, the car financing company, is set to receive up to $5.6bn in a new capital injection from the Treasury, filling a hole identified in the “stress tests” earlier this year and paving the way for the government to become the majority shareholder.

The company, formerly the financing arm of General Motors, was one of 19 institutions to submit to a capital adequacy programme led by the Federal Reserve and completed in May. That determined that GMAC had a shortfall, which will now be provided by the government in the form of preferred equity, according to two people familiar with the situation.