Existing U.S. home sales rose in December and unsold inventories declined, the National Association of Realtors said Friday. The trade group said sales of single-family homes, townhomes, condominiums and co-ops rose 5 percent to a seasonally adjusted annual rate of 4.61 million in the month. Inventories, meanwhile, fell 9.2 percent to 2.38 million existing homes available for sale. The supply of homes on the market represented an 6.2-month supply at current market conditions. \"The inventory supply suggests many markets will see prices stabilize or grow moderately in the near future,\" said NAR Chief Economist Lawrence Yun. NAR said investors purchased 21 percent of homes in December, up from 19 percent in November and 20 percent in December 2010. First-time buyers fell to 31 percent of the purchasers in December from 35 percent in November and 33 percent a year earlier. For December, median prices around the country ranged from $129,100 in the Midwest to $231,300 in the Northeast. In the South, the median price was $146,900. In the West, the median price for existing homes in December was $205,200.