No, IBKR does not charge clients for SMS/text messages.
However, normal messaging charges from your provider may apply.
Do you charge for SMS?
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Are Stock Yield Enhancement Program loans made only in increments of 100?
Are custody fees charged on bond positions held through IBKR?
Do you charge a fee for an IRA account transfer out?
Is there a separate IBKR Mobile app for IBKR Lite?