The number of new home purchases nationwide rose 11 percent in June from May, according to figures released today by the Commerce Department. That jump is the largest in eight years and brings sales to an annual pace of 384,000. Even as home sales rose, the median new home price fell to $206,200 from $219,000 in May. Compared to June 2008, new home sales were down 21 percent and home prices fell 12 percent. But the numbers suggest that the housing market may finally be stabilizing, economists said. Economists had predicted that home sales would rise to 352,000 in June, according to a Bloomberg News survey.