General Motors Co. will purchase 200 million shares of its stock from the U.S. Treasury as part of the department’s plan to sell its entire holding of GM stock within 15 months.

The $5.5 billion transaction, at $27.50 a share, represents a 7.9 percent premium and will close by the end of the year, GM said. Treasury plans to begin selling its remaining shares as soon as January, the company said. The sale represents 40 percent of the government’s remaining stake after the 2009 bailout and 2010 initial public offering.