NEW YORK (CNN/Money) - Long-term mortgage rates sank to a fresh six-month low this week, Freddie Mac reported Thursday.

The rate on 30-year fixed-rate mortgages averaged 5.64 percent in the week ended Thursday, with an average 0.7 of a point payable up front, down from last week when it averaged 5.69 percent.

A year earlier, the rate on the 30-year fixed-rate loan stood at 6.05 percent.

The 15-year mortgage rate eased to 5.01 percent this week from 5.07 percent last week, also with 0.7 of a point up front. Last year, the average rate stood at 5.39 percent.

"Home sales are very sensitive to mortgage rates," said Frank Nothaft, Freddie Mac chief economist. "Low mortgage rates drove the uptick in sales during September.

"And with mortgage rates at their lowest level in six months, home sales should continue strong through the autumn months," Nothaft said.

Rates haven't been this low since April 1, when the 30-year fixed-rate stood at 5.52 percent and the 15-year was at 4.84 percent.

One-year adjustable rate mortgages (ARMs) averaged 3.96 percent, down from 4.02 percent the previous week, with 0.8 of a point payable up front. ARMs are now at their lowest rate of the year since late May 27, when rates averaged 3.87 percent.

At this time last year, the average rate for ARMs was 3.76 percent.

"Our latest forecast expects a brisk housing industry through year-end. Single-family building is likely to remain strong this quarter, as evidenced by the pace of recent new-home sales," Nothaft added.

"Overall, the economy remains supportive of both new and existing homes."

Freddie Mac (down $0.50 to $65.98, Research)'s average mortgage rates are based on a survey of 125 lenders nationwide.