WASHINGTON — U.S. home prices jumped in September as strong demand, low interest rates and the smallest number of available homes on record combined to push up housing costs. 

The S&P CoreLogic Case-Shiller 20-city home price index, released Tuesday, showed that home prices rose 6.6% in September from a year earlier, much higher than its 5.3% increase in August. That is the biggest increase since April 2018.

The viral pandemic disrupted the spring home buying season, pushing many sales into the late summer and fall. Home sales jumped to the highest level in 14 years in September, a sign that the increased ability of some Americans to work from home and the desire for more space is spurring greater demand. 

Prices skyrocketed 11.4% in Phoenix compared with a year earlier, the biggest gain nationwide. Seattle reported the second highest increase, at 10.1%, followed by San Diego at 9.5%. 

The number of homes for sale sank in September to the lowest level since records began in 1982, according to the National Association of Realtors. And last week mortgage rates fell to a record low of 2.72%, according to mortgage buyer Freddie Mac. 

Home prices are rising broadly across the country. In September, 19 cities in the S&P 20-city index reported bigger price gains compared with a year ago than in August. The 20th city, Detroit, has reported delays at its recording office because of the pandemic and did not have enough data to calculate price changes.