Sales of existing U.S. homes fell in June for the eighth time in the past 10 months while home prices rose at the slowest pace in more than a decade, the National Association of Realtors (NAR) said Tuesday in its report. Sales of previously owned homes and apartments fell 1.3 percent in June to an annual rate of 6.62 million units. The decline, in line with expectations, was the third consecutive drop and the eighth in the past 10 months as the U.S. housing market has shifted to a slower pace due to rising mortgage rates. According to the report, the inventory of unsold homes rose to a new record of 3.725 million units, which is a 6.8 month supply at the June sales pace. Analysts believe that the growing number of unsold homes will further depress prices in coming months. The median price of a home sold last month was up only 0.9 percent from June 2005 and represented the smallest 12-month price gain since mid-1995.