Sales of existing homes, depressed by turmoil in credit markets, fell for a sixth consecutive month in August to their lowest level in five years, and the decline in U.S. home prices accelerated in July, posting the steepest drop in 16 years, two reports showed Tuesday. The National Association of Realtors (NAR) said that sales of existing single-family homes fell by 4.3 percent in August to an annual rate of 5.5 million units, the slowest pace since mid-2002. The decline in sales increased the inventory of unsold homes to a record 4.58 million in August, meaning that it would take 10 months to exhaust the inventory of homes on the market at the August sales pace, also a record figure. Meanwhile, the S&P/Case-Shiller home price index showed that prices have fallen by more every month since the beginning of the year. The index of 10 U.S. cities fell 4.5 percent in July from a year ago, the biggest drop since mid-1991. A broader index of 20 cities fell 3.9 percent in July from last year, with 15 cities reporting that prices fell. The five cities where prices are still rising-Atlanta, Charlotte, Dallas, Portland, and Seattle-have reported growth is slowing in the past year. Atlanta and Dallas are close to moving into negative territory, S&P said. “The further deceleration in prices is still apparent across the majority of regions,” economist Robert Shiller said in a statement. The U.S. housing market has been battered by the steepest downturn in 16 years. The problems were made worse in August by turmoil in credit markets, reflecting new concerns about rising defaults in “sub-prime” mortgages. Many analysts believe that sales and prices will fall further as the housing market receives additional blows from rising default rates that are putting even more homes on an already glutted market and causing lenders to tighten standards. Such factors have made it more difficult for potential borrowers to qualify for loans.