LOS ANGELES — The average long-term U.S. mortgage rate climbed to a six-week high this week, pushing up borrowing costs for homebuyers already facing the challenges of rising housing prices and a shortage of homes for sale.

The average rate on a 30-year mortgage rose to 6.69% from 6.6% last week, mortgage buyer Freddie Mac said Thursday. A year ago, the rate averaged 6.13%.

As mortgage rates rise, they can add hundreds of dollars a month in costs for borrowers, limiting how much they can afford.

Rates have increased three out of four weeks this month. The latest uptick brings the average rate to its highest level since December 14, when it was 6.95%.

Borrowing costs on 15-year fixed-rate mortgages, popular with homeowners refinancing their home loans, also rose this week, lifting the average rate to 5.96% from 5.76% last week. A year ago, it averaged 5.17%, Freddie Mac said.

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