Mortgage applications rose for the first time in five weeks as filings for home purchases rebounded, according to a private group’s survey.

The Mortgage Bankers Association said yesterday that its index of applications to buy a home or refinance an existing mortgage rose 9.9% to 600.1 last week, the biggest gain since mid-June, from 545.9 a week earlier.

The combination of rising incomes and borrowing costs that are still historically low will keep housing demand from collapsing, even as rising home prices have put purchases out of reach for some buyers, economists said. The average 30-year mortgage rate fell to 6.08%, the lowest in more than two months, from 6.15% a week earlier.

“Home buying is at relatively high, although no longer robust levels, while refinancing activity has slumped despite its rebound in the last two weeks,” the president of Insight Economics, Steven Wood, said. “Less refinancing activity should dampen consumer spending – although that has not yet occurred.”

The mortgage bankers group’s measure of purchases rose 9.3% to 457.4 from the prior week’s reading of 418.3, which was the lowest since February 18.

American homebuilders’ shares on January 9 had their biggest gain since October 1, 2003, led by D.R. Horton and Centex Corporation, after Merrill Lynch & Company said “long-term” demand will support the real estate market. The Standard & Poor’s homebuilders index of 16 companies rose 5.7%, and has risen 30% the past 12 months.

Fort Worth, Texas-based D.R. Horton, the largest American homebuilder, said orders increased 19% during the fiscal first quarter ended December 31.

“Our continued sales momentum and record first-quarter backlog position the company for another record year,” the company’s chairman, Donald Horton, said in a statement.

The mortgage bankers group’s gauge of refinancing jumped 9.9% to 1497.5, the biggest gain since the week ended July 1.

At the current 30-year average rate, the cost for every $100,000 of a loan would be $604.70 a month. When the rate, as measured by the Mortgage Bankers Association, was at a record low of 4.99% in June 2003, the cost was $536.21 a month.

Even with last week’s rise in purchase applications, economists forecast housing demand will slow this year from last and restrain economic growth.

The economy will grow at a 3.4% annual rate this year, the median forecast in a Bloomberg News survey of 72 economists December 23 to January 9, down from an estimated 3.6% in 2005.