Mary Bailey, a 79-year-old widow in Arlington, Mass., made a big deposit for her grandchildren at her Citizens Bank branch when a financial adviser there sold her on a newfangled $100,000 certificate of deposit. It would, he said, double her savings in six years, according to a later state enforcement action.

So she was irate when her first statement showed the CD’s value had fallen to $95,712, thanks to upfront fees. “This was not a CD as I know a CD,” Ms. Bailey says.

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