I imagine the ‘paid family account’ would work like this:
Price
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Fixed monthly fee for the account.
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Up to a certain amount of cards for free (maybe 3 free cards included).
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One time fee for additional cards.
I think the cost of running an account of this type wouldn’t be more than the cost of running a regular current account (ie: slightly positive), except the one time cost of the cards. So Monzo would make a large percentage of profit from the monthly fee.
Features
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Pot like “mini accounts” for each card with independent transaction feeds and categorisation.
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Ability to set limits on those cards and possibly approval of online payments by an administrator account.
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Perhaps a separate app.