WASHINGTON (Reuters) - U.S. existing home sales rebounded sharply in October, posting the first annual gain since mid-2021, as buyers rushed into the market to take advantage of a brief decline in mortgage rates.

Home sales jumped 3.4% last month to a seasonally adjusted annual rate of 3.96 million units, the National Association of Realtors said on Thursday. Economists polled by Reuters had forecast home resales rebounding to a rate of 3.93 million units. Sales slumped to a rate of 3.83 million units in September, which was the lowest since October 2010.

Sales increased 2.9% year-on-year, the first annual rise since July 2021.

"The worst of the downturn in home sales could be over, with increasing inventory leading to more transactions," said Lawrence Yun, the NAR's chief economist.

October's homes sales likely reflected contracts signed in August and September, when mortgage rates were declining in anticipation of the Federal Reserve launching its policy easing cycle. The U.S. central bank cut its policy rate by an unusually large half-percentage-point in September, its first reduction in borrowing costs since 2020.

The Fed delivered another 25 basis points reduction this month, which lowered its benchmark overnight interest rate to the 4.50%-4.75% range.

Mortgage rates have erased all the decline since August as U.S. Treasury yields have risen on strong economic data and investor fears that President-elect Donald Trump's policies, including higher tariffs on imported goods and mass deportations, could reignite inflation.

Mortgage rates track the 10-year Treasury note. The average rate on a 30-year fixed-rate mortgage has jumped to 6.78% last week from 6.08% in late September, data from mortgage finance agency Freddie Mac showed. The Fed hiked rates by 525 basis points in 2022 and 2023 to tame inflation. 

Housing inventory rose 0.7% to 1.37 million units last month. Supply increased 19.1% from one year ago.

Despite the rise in inventory, the median existing home price rose 4.0% from a year earlier to $407,200 in October. That was the highest for any October. Home prices rose in all four regions.

At September's sales pace, it would take 4.2 months to exhaust the current inventory of existing homes, up from 3.6 months a year ago. A four-to-seven-month supply is viewed as a healthy balance between supply and demand.

Properties typically stayed on the market for 29 days in October compared to 23 days a year ago. First-time buyers accounted for 27% of sales versus 28% a year ago.

That share remains below the 40% that economists and realtors say is needed for a robust housing market.

All-cash sales made up 27% of transactions, down from 29% a year ago. Distressed sales, including foreclosures, represented only 2% of transactions, virtually unchanged from last year.