"It's truly expensive to be poor," said Daniel H. Schulman, a group president for enterprise growth at American Express.One woman kept her savings — a $100 bill — in the freezer. Another, a single mother in Texas, said she had only enough extra cash each week to buy one wooden letter, for $3, to spell out her daughter’s name on her bedroom wall. A third, a housekeeper in Brooklyn, lives in a homeless shelter.

These are not the customers a big bank would normally covet, let alone cater to. But an increasing number of the nation’s biggest lenders are doing just that, devising low-fee banking especially for customers with troubled finances. The products, including bare-bones bank accounts and prepaid debit cards, are hardly big money makers — in some cases, the banks barely break even.

But for the banks working to overhaul their public images in the aftermath of the financial crisis, the products offer a different and potentially far bigger payout: good will from regulators and a chance to woo more customers who might just become profitable in the long run.

The products, some regulators say, might help coax back into the banking system people like Neighborhood Trust client Esther Guzman, the housekeeper living in a Brooklyn homeless shelter, who said she had to abandon her bank account after running up nearly $700 in overdraft fees.

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