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The median price of single-family homes sold in King County leapt in March to $392,000 as buyers, many waving all-cash offers, bid up the region’s tight inventory.

With 40 percent fewer houses for sale than a year ago, March’s median closing price was 19 percent higher than the previous March and up 7 percent from February, the Northwest Multiple Listing Service reported Thursday.

It was the biggest monthly percentage gain since April 2012, when King County’s median home price started rising after 19 months of decline.

A severe shortage of homes for sale — with listings equal to only about a month’s worth of pending sales — is driving the jump in prices. Generally a supply of four to six months is considered a balanced market.

“Where are the listings?” asked Glenn Crellin, associate director for research at the University of Washington’s Runstad Center for Real Estate Studies. Crellin said the inventory over the past four months is the lowest he’s seen in the 15 years he’s been tracking it.

“That’s going to be a real problem now that we’re heading into the prime buying season, and there is just so little product available for sale,” Crellin said.

About a quarter of buyers are paying all cash for homes, said OB Jacobi, president of Windermere Real Estate in Seattle. The rest are putting down, on average, between 20 and 50 percent cash, he said.

“I think that is pretty shocking,” Jacobi said. “It’s crazy.”

Foreclosed properties are drawing an even higher rate of all-cash offers. Seattle real-estate broker Keith Brown, who sells only foreclosed homes, estimated that roughly half the offers on a property he lists are all cash.

“I’m not quite sure where everyone is coming up with all this cash, but there’s definitely been a huge increase in the last few months,” Brown said.

All regions in King County saw a lift in median prices:

In Seattle, the median price of single-family homes sold rose 17 percent to $462,375, the MLS reported. The median for condos was $292,500, almost 25 percent higher than a year ago.

On the Eastside, the median sale price of single-family homes also jumped 17 percent to $552,415, but condos didn’t rise as much: an 11 percent increase to $234,000.

Price jumps happened at every tier of the housing market.

In middle-class West Seattle, the median sale price on more than 100 homes sold in March was $365,372, almost 30 percent higher than the previous March.

Meanwhile, in affluent West Bellevue, the median sale price on the 34 homes sold last month was nearly $1.3 million, 23 percent higher than a year ago.

Snohomish County mirrored the price hikes in King County: The median selling price for single-family homes rose 17 percent in March to $287,825, and for condos, $149,500.

Experts say the spike in demand will draw more sellers into the market.

For one thing, banks that were sitting on foreclosed homes last year amid allegations of improper foreclosures are starting to sell that inventory, said Brown.

“We have 50 percent more properties in our inventory than we did six months ago,” he said.

Rising home prices also should encourage some homeowners to sell, brokers say.

And homebuilders are ramping up production in response to demand.

In the Seattle metro area, building permits were issued in January and February for more than 1,300 single-family homes, a 41 percent increase over the same period last year, according to the latest census data.

Homebuilders are struggling to find enough laborers and subcontractors because so many left the industry during the Great Recession, said Allison Butcher, a spokeswoman for the Master Builders Association of King and Snohomish Counties. Municipal permitting staffs, which were slashed during the recession, also are playing catch-up, she said.

Perhaps the biggest question is how long the run-up in home prices could last, stoked by ultralow interest rates and a shrinking supply of buildable land. The state’s growth-management act puts many areas off-limits to development.

Mark Mason, CEO of HomeStreet Bank in Seattle, said the tight home inventory and insufficient supply of land approved for development will affect the bank’s business. “We’re concerned that most potential borrowers will not be able to buy homes,” he said. “If that demand is not satisfied, we can’t write mortgages.”

The frenzied home market has had one benefit for the bank: A flood of prospective borrowers have come the past three months to get prequalified on a home loan — nearly three times last year’s average, Mason said.

All of which could make this spring buying season the busiest in years, if inventory remains tight and more buyers enter the market.

“My guess is it’s going to be frenzied at least through the summer,” Jacobi said.

Sanjay Bhatt: 206-464-3103 or On Twitter @sbhatt