I am not putting it into a savings account and earning any interest on my money. I am simply keeping it in a checking account without earning any interesting. But having my money mixed up with the bank, is this haram?
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As long as there is no other Islamic alternative, you are not sinful as this is the only means to protect your money.

I am living in the United States. All of the banks I have access to are based on riba (interest) and are haram. Does keeping my money in this bank make my money haram?