Washington ? Existing homes were sold at the fastest pace in history last month, and the median price set a record as well. But some private economists predicted housing may be nearing its peak as mortgage rates begin to rise.

In June, existing homes sold at an annual rate of 7.33 million units, an all-time high and an increase of 2.7 percent from the seasonally adjusted sales pace in May, according to a report Monday from the National Association of Realtors.

The gain reflected a 2.4 percent rise in sales of single-family homes, which climbed to a record annual rate of 6.37 million units. Sales of condominiums also set a record, rising by 4.5 percent from the May level to an annual rate of 966,000 units in June.

The strength in sales helped pushed the median price of an existing home to a new record of $219,000, a gain of 14.7 percent from the median, or midpoint, for homes sold a year ago. That was the biggest jump in prices in nearly 25 years.