…Home purchases in the three months through September jumped 32 percent from a year earlier to 534, the most for a third quarter since 2005, appraiser Miller Samuel Inc. and brokerage Douglas Elliman Real Estate said in a report today….

…“This is the next step in the rebound,” Jonathan Miller, president of New York-based Miller Samuel, said in an interview….

…Luxury homes in the Hamptons, the top 10 percent of deals by price, sold for a median of $4.45 million in the third quarter, up 14 percent from a year earlier, Miller Samuel and Douglas Elliman said….

…Buyers are rushing to make deals before expected increases in mortgage rates, propping up the lower end of the market, according to Miller….

…Hamptons home prices have gained 14 percent from their bottom in the first quarter of 2009, when sales stalled during the credit crisis and listed properties piled up to the point that selling them all would have taken almost three years, Miller Samuel data show….

…Third-quarter listed inventory was 1,656 homes, compared with 1,302 a year earlier, according to Miller Samuel and Douglas Elliman data….