The average price of existing single-family homes in King, Snohomish and Pierce counties increased 0.7 percent in August over the month.That was a big change from July, when Seattle metro’s price was down 0.1 percent over June.

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Seattle metro home prices rose strongly in August and outpaced gains nationally, according to the S&P/Case-Shiller 20-city index released Tuesday.

The average price of existing single-family homes in King, Snohomish and Pierce counties increased 0.7 percent in August over the month after seasonal adjustment. That was a big change from July, when Seattle metro’s average price was down 0.1 percent over June.

The 20-city composite index was up 0.1 percent in August over the month, compared with a 0.2 percent slide in July. Eleven metros posted monthly gains, five lost ground and four recorded no change.

With a 0.9 percent monthly gain, the Portland metro area posted the largest increase in August. Average price increases in Dallas and Denver also led the index, with monthly gains of 0.8 percent and 0.7 percent, respectively.

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Over the year, Seattle metro’s home prices gained 7.6 percent, the fifth-highest annual increase among the 20 metros. The 20-city index posted a 5.1 percent gain over the year.

Denver and San Francisco tied for the largest annual gain, at 10.7 percent, followed by Portland, at 9.4 percent. New York, Washington, D.C., and Chicago all posted annual gains of less than 2 percent, trailing the other metros.

David Blitzer, chairman of the index committee for S&P Dow Jones Indices, said the 5.1 percent national increase means more now than during the peak of the last housing boom a decade ago because of today’s low inflation rate. Through September, core inflation, excluding food and energy, was 1.9 percent.

“The rebound from the recent lows was faster than the 1997-2005 housing boom, and also much less driven by inflation,” Blitzer said in a statement.

Home prices, as measured by the Case-Shiller index, have yet to recover all the ground lost since the last peak.

In the Seattle area, prices are about 4 percent below the market’s prior peak; the 20-city index is about 12 percent off.

Seattle-based Zillow, which also tracks home prices, said the median home price of single-family homes in King, Snohomish and Pierce counties in August was $374,600, up 7.6 percent over the year. Zillow’s index includes all homes in a market, using recent sales as one of several factors in estimating price trends.

“Annual U.S. home value appreciation has stabilized and settled into a nice groove over the past few months with steady appreciation,” Zillow Chief Economist Svenja Gudell said in a statement. “This relative stability should continue into the foreseeable future.”

“Interestingly, a good portion of the overall home price growth we’re seeing, especially in cities, has been driven by strong growth in condominium values, which are currently appreciating more quickly than single-family homes,” Gudell said. “This is a sign of the times in terms of buyers’ preferences, as condos often represent a more affordable, more urban housing option that is particularly attractive to younger buyers.”