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U.S. home prices have fully recovered from their steep plunge during the housing bust and Great Recession, according to a private measure.

The Standard & Poor’s CoreLogic Case-Shiller national home price index, released Tuesday, is slightly above the peak it set in July 2006, after rising 5.5 percent in September from a year earlier. The milestone comes after more than four years of steady gains.

Still, prices have not fully recovered in many cities and other gauges show that home prices remain below their peaks.

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