Using the social security number of the minor on a "minor by" account could lead to the IRS treating the account as an attempt at tax evasion. My advice? Don't set up "minor by" accounts. Further, I agree with Randy. They are a no-man's land in case of dispute. And likely a no-man's land with respect to FDIC insurance coverage. Your customer may requests them. Your bank may have opened them for years. You may have never had trouble with your minor by accounts, But if you've never had trouble, you've likely never had a dispute or the scrutiny of the IRS.
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