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For the first time, the federal government will back mortgages of more than $1 million, a move that reflects the run-up in home prices across much of the nation.

The Federal Housing Finance Agency (FHFA) on Tuesday said the maximum size of home-mortgage loans eligible for backing by Fannie Mae and Freddie Mac will jump to $1.089 million next year in high-cost markets. In most other markets, the maximum size of mortgages eligible for backing will be $726,200 in 2023, an increase of 12% from current limits, the agency said.