WASHINGTON — U.S. long-term mortgage rates continued to fall this week, reaching their lowest levels in nine months.

The decline in home borrowing rates in recent weeks has been a spur to prospective homebuyers, reflected in a spike in applications for mortgages. Mortgage buyer Freddie Mac says the average rate on the benchmark 30-year, fixed-rate mortgage dipped to 4.45 percent this week from 4.51 percent last week.

Rates remain far above last year’s levels, however. The key 30-year rate averaged 3.99 percent a year ago.

The average rate for 15-year fixed-rate loans fell to 3.89 percent from 3.99 percent last week.

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