It occurs to me that checking accounts, especially free ones, have always tended to be the "loss leaders" of a bank's marketing strategy. It's like when your grocery store sells milk at a sale price lower than their own cost, then shelves the milk all the way in the back, hoping that you'll see a whole cartload of things you "need" at normal prices on your way in and out. They're trying to take advantage of your need for milk, and hoping you don't take advantage of their marketing strategy.
When customers start making that long walk to the dairy case, grabbing a gallon of milk, and checking out without making a single other purchase, stores have the option of putting fine print in the ads for the next sale: "with minimum $10 purchase." Or, they can assume that even the "milk-only" customers are getting a good look at what the store has to offer, and will eventually build an ongoing business relationship.
Your call, for future offers. But grabbing the milk out of the hands of every person who takes advantage of your marketing strategy tends to make you look unattractive. I don't recommend it.
Besides, how much of a drain is this person? True, she's not keeping money in the bank long enough for you to lend it out at interest, but that's true of all demand deposit accounts. She also isn't using up the time of, for example, your check order department, item processing, signature verification, etc.
Could you call it a draw?
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Opinions expressed do not necessarily reflect those of my employer or of my cats.