NEW YORK (CNN/Money) - Long-term mortgage rates headed higher for the first time since Sept. 5 as employers expanded their payrolls in September and job losses in August were revised sharply downward, indicating better days may lie ahead for frustrated job seekers.

The 30-year mortgage rate rose to 5.95 percent in the week ending Oct. 10, with an average of 0.6 point payable up front, up from 5.77 percent last week. The 30-year stood at 5.98 percent at this time last year, according to mortgage finance company Freddie Mac.

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The 15-year fixed-rate mortgage climbed to 5.26 percent, up from 5.10 percent a year earlier. The 15-year averaged 0.6 point payable up front. A year ago, the 15-year rate stood at 5.34 percent.

But the rate on one-year adjustable-rate mortgages (ARMs), loosely indexed to the 10-year Treasury note, fell to 3.69 percent, with 0.6 point, from 3.72 percent last week. That rate is below the year-ago rate of 4.23 percent.

"Not only did the market get good news about September employment last week, but it was further bolstered by the upward revision of jobs in August," said Frank Nothaft, Freddie Mac chief economist. "This inspired a little optimism in the market that we may have bottomed out as far as job losses are concerned."

"Freddie Mac economists expect the economy will grow about 4 percent in 2004, but since inflation will remain very low, mortgage rates should average somewhere just above 6 percent to 6.25 percent over the next year," he added.

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Freddie Mac's average mortgage rates are based on a survey of 125 lenders nationwide. The rates include those on mortgages accepted by borrowers with good credit ratings who place a 20 percent down payment on their homes, according to Freddie Mac. The total amount of each mortgage considered for the survey doesn't exceed a $322,700 limit.

Freddie Mac (FRE: up $0.75 to $57.30, Research, Estimates), or Federal Home Loan Mortgage Corp., is a publicly traded company the government established in 1970 to provide a flow of funds to mortgage lenders. It buys mortgages from banks, bundles them and then resells them as mortgage-backed securities.

Its products, and the products of other similar entities, have become increasingly popular as an alternative to government-backed bonds, particularly with international investors.