WASHINGTON — To coax more lenders to participate, the government on Wednesday said it would overhaul a program designed to help struggling borrowers stay in their homes.

The Hope for Homeowners program will require lenders to write down loans only to 96.5% of market value if the borrower's debt-to-income ratio is below 31%. For loans to higher debt-to-income borrowers, lenders would have to stick to the original writedown mandate of 87% to qualify.

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