WASHINGTON >> 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 said today 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.

The recent easing of rates has come amid steep declines in the stock market and tumbling interest rates on the 10-year U.S. Treasury note — which influences long-term mortgage rates.

The decline in rates could help boost home sales, which stumbled last year as higher borrowing costs eroded affordability.

Mortgage applications jumped 23.5 percent in the week ended Jan. 4 from a week earlier, according to the Mortgage Bankers Association. Experts say the rebound in applications followed a slower-than-usual holiday period, and the slide in mortgage rates also prompted a flurry of refinancing, especially by borrowers with larger mortgage loans.

The MBA’s refinance index rose 35 percent in the week ended Jan. 4, reaching its highest level since July 2018.

To calculate average mortgage rates, Freddie Mac surveys lenders across the country between Monday and Wednesday each week.

The average doesn’t include extra fees, known as points, which most borrowers must pay to get the lowest rates.

The average fee on 30-year fixed-rate mortgages was unchanged this week at 0.5 point. The fee on 15-year mortgages held steady at 0.4 point.

The average rate for five-year adjustable-rate mortgages dropped to 3.83 percent from 3.98 percent last week. The fee rose to 0.3 point from 0.2 point.