Two U.S. housing reports released Wednesday morning show more signs of improvement in the housing market, suggesting that it might finally be on its way toward a full recovery.

The National Association of Realtors reported that existing-home sales rose 7.8 percent to a seasonally adjusted annual rate of 4.82 million in August and the national median home price rose on a year-over-year basis for the sixth month in a row.

The Commerce Department reported that housing starts increased 2.3 percent in August to a seasonally adjusted annual rate of 750,000 and building permits, an indicator of future building activity, fell 1 percent to a seasonally adjusted annual rate of 803,000.

“The housing market is steadily recovering with consistent increases in both home sales and median prices,” Lawrence Yun, NAR chief economist, said in a statement. “The strengthening housing market is occurring even with difficult mortgage qualifying conditions, which is testament to the sizable stored-up housing demand that accumulated in the past five years.”

Existing-home sales, which include single-family homes, townhomes, condominiums and co-ops, were up from 4.47 million in July and 4.41 million in August 2011.

The national median existing-home price for all housing types was $187,400 in August, an increase of 9.5 percent from August 2011. The increase was the strongest since January 2006 when the median price rose 10.2 percent from a year earlier.

According to RealEstate Business Intelligence, the median sales price in the D.C. metro area was $385,000 in August, up 8.15 percent from a year ago August.

The Northeast led the country in increased existing-home sales as sales in that area rose 8.6 percent in August. Sales in the West rose 8.3 percent, in the Midwest 7.7 percent and in the South 7.3 percent.

Last week, the Federal Reserve announced its biggest stimulus action in two years. Although this move is expected to lower mortgage rates — the current 30-year fixed-rate average is around 3.5 percent — would-be homebuyers continue to struggle with higher down payment and credit score requirements.

“Total sales this year will be 8 to 10 percent above 2011, but some buyers are frustrated with mortgage availability,” NAR president Moe Veissi said in a statement. “If most of the financially qualified buyers could obtain financing, home sales would be about 10 to 15 percent stronger.”

Although the increase in residential construction was not as robust as some economists had expected it to be, it was up 29.1 percent compared to August last year.

Single-family housing starts fueled the increase. That sector increased 5.5 percent to a seasonally adjusted annual rate of 535,000, the highest since 2010 just before the home buyer tax credit expired. Single-family housing starts have climbed more than 100,000 in the past year.

The National Association of Home Builders/Wells Fargo Housing Market Index has risen from 14 in September 2011 to 40 in September 2012, its highest level in more than six years. The index hasn’t gone above 50 since April 2006. An index of 50 or better indicates builders view market conditions more positively than negatively.

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