WASHINGTON (AP) — U.S. home sales climbed 3.6% in December, but a record-low inventory of houses on the market has caused prices to surge as affordability is worsening.

The National Association of Realtors said Wednesday that sales of existing homes rose last month to a seasonally adjusted annual rate of 5.54 million. For all of 2019, 5.34 million homes were sold — matching the 2018 level. High mortgage rates hurt sales in the first half of the last year, while lower rates boosted purchases in the second half.

But the rebound in sales failed to cause more people to put their homes on the market. Sales listings have tumbled 8.5% from a year ago to 1.4 million properties. There are just 3 months' supply of single-family houses for sale, the lowest level since the Realtors began tracking the number in 1982. Inventories have fallen at all price levels below $1 million for the past year.

The median sales price has jumped 7.8% over the past year to $274,500. Home values have increased at more than double the pace of wage growth, making it harder for would-be buyers to save enough money for a down payment.

In December, sales rose in the Northeast, South and West. But sales fell in the Midwest, which is generally a more affordable market.