Bank of America Corp. is rolling out a new-mortgage product that would allow borrowers to make down payments of as little as 3%, in a move that would represent an end run around a government agency that punished the bank for making errors on similar loans.

The new mortgage program, which the Charlotte, N.C.-based lender plans to unveil on Monday, will let borrowers avoid private mortgage insurance, a product to protect mortgage lenders and investors that is usually required for low-down-payment loans.

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