More than half of the borrowers who received loan modifications on delinquent mortgages defaulted again after nine months, according to a federal report.

The re-default rate of loans modified in the first quarter of 2009 was 51.5 percent by the end of the year, the Office of the Comptroller of the Currency and the Office of Thrift Supervision said in a joint report Thursday. The figure, which measures payments at least 30 days late, climbed to 57.9 percent for changes made in the prior 12 months.

Homeowners are struggling to make payments as depressed housing prices leave them owing more than their properties are worth. About 24 percent of properties with a mortgage were underwater in the fourth quarter, First American CoreLogic said last month. The median price of a U.S. home was $165,100 in February, down 28 percent from its peak in July 2006, according to the National Association of Realtors.

Modifications are “clearly not working well and it’s not a surprise,” said Sam Khater, a senior economist at First American CoreLogic. “It’s pointless to rewrite these loans because they’re underwater.”

The number of homes with mortgage payments at least 60 days late climbed to 2.39 million in the fourth quarter, up 13.1 percent from the prior three months and 49.6 percent from the year-earlier period, a Mortgage Metrics report said.

About 4.5 million foreclosure filings are expected in 2010, according to RealtyTrac Inc., a seller of default data.