Millennials, it seems, like to share everything about themselves, from selfies on Facebook and Instagram to how much money they spent at the pub last night. It’s one reason the person-to-person payment app Venmo — which encourages users to share spending habits with friends — is so popular with the 18-to-34-year-old crowd.

But in rebranding and reintroducing a P-to-P payments service, the nation's biggest banks are targeting a broader demographic and betting that people who came of age in the 1980s and 1990s want to be more private about how they spend their money.

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