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Apple Pay can be used in stores and for online purchases. Would it be a far cry to expect it to be used in banks? I can use my debit card rather than a deposit slip to deposit checks at the bank counter, so why not my iPhone?
Maybe you already can. Some banks offer the ability of depositing checks simply by taking a picture of the check.
All depends on what Apple can hammer out with the banks. There's financial gain for them to be involved with purchases but not so much with deposits.