I own a pet-sitting business. Can I charge clients interest if they don't pay within, say, a month?
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If you could get away with that, your clients could just as easily come back to you and say, "I'm not paying you $100 per dog sit; I'm only paying $50," and you'd have to stick with that.
However, if you had a written agreement (that they signed) stating your fees and that interest would be charged on late payments, then yes, you would be entitled to collect, because it's part of your contract.
Even better, get the client to agree (in writing) to monthly charges to a valid credit card. That way, you won't have to deal with late payers.