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Home prices through the roof - biggest jump in 7 years 

U.S. home prices went through the roof in April, posting their biggest monthly gain in seven years.

If that wasn't enough of a sign the housing market is roaring back, sales of new single-family homes in May rose to their highest monthly level in nearly five years.

"The recovery is definitely broad based," said David Blitzer of S&P Dow Jones, which released the latest S&P/Case-Shiller Home Price Indices, showing that from March to April, home prices gained 2.6 percent in the top ten U.S. housing market and 2.5 percent in the top 20 market.

The average prices rose 11.6 percent and 12.1 percent in each market in April from a year ago, the indices said.

"The two composites showed the largest year-over-year gains in seven years," said Blitzer,

As of the end of April 2013, average home prices across the nation are back to levels of early 2004. But they are still down between 26 and 27 percent from their peaks in the summer of 2006, the report noted.

Also on Tuesday, the Commerce Department said sales of new single-family homes rose to their highest level in nearly five years in May, confirming the housing market's strengthening tone. It said sales increased 2.1 percent to a seasonally adjusted annual rate of 476,000 units - the highest level since July 2008. It was the third straight month of gains in new home sales.

Sales had increased 3.3 percent in April. Economists polled by Reuters had expected new home sales to rise to a 462,000-unit rate last month.

Compared with May 2012, sales were up 29 percent, the Commerce Department said.

(Read More: Rising Home Prices Are 'Unsustainable'-Realtors)

According to the S&P/Case-Shiller home price figures, Atlanta, Las Vegas, Phoenix and San Francisco posted year-over-year gains of over 20 percent in April, with San Francisco leading the way at 23.9 percent. Phoenix posted 12 consecutive months of double-digit growth, as investors there continue to compete for what few distressed properties are for sale.

Inventories did rise in Phoenix in May slightly, but demand is still outstripping supply, and pushing prices higher, the report said.

(Read More: Home Builders Slow New Construction, Raise Prices)

Concerns about rising mortgage rates, which spiked in to the mid-4 percent range in just the past week, have dampened expectations for home price gains this summer. Analysts also worry that prices are rising too fast, far faster than income growth, and will soon price too many potential buyers out of the housing market.

"Today's Case-Shiller numbers may reflect where the housing market has been in some of the frothier metros, but they are not indicative of where it's headed," said Zillow Chief Economist Dr. Stan Humphries.

"The housing market worm has turned over the past few weeks – inventory levels are beginning to show signs of easing, and mortgage interest rates are creeping up. Both of these factors will help mitigate extreme price spikes caused by very strong housing demand and very low housing supply," Humphries said.

This latest report only tracks prices on a three-month moving average through the end of April, well before mortgage rates began their climb. Still Blitzer contends rising rates will not slow price gains.

"Home buyers have survived rising mortgage rates in the past, often by shifting from fixed rate to adjustable rate loans. In the housing boom, bust and recovery, banks' credit quality standards were more important than the level of mortgage rates.

"The most recent Fed Senior Loan Officer Opinion Survey shows that some banks are easing credit restrictions. Given this, the recovery should continue," he said in the report.

(Read More: Mortgage Cop: Four Top Banks Fail Consumers)

(Reuters contributed to this report)

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