Real Estate Law
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I hate to bring you potentially bad news, but it is VERY common for late fees and interest on missed payments to be part of the paperwork given to the customer when signing up for whatever is being purchased--services or goods bought on payments.
There is no law requiring that such notice be on the bills themselves. There is no way to know for sure if what you describe is allowed without also seeing that paperwork.
I would be shocked (at sloppy management and document preparation) if late fees and interest were not in your paperwork. You might want to take a look there.
To be more explicit, Yes, this is usually legal.
Due dates have meaning and consequences. If the specific charges and ways they get imposed are in the sign-up paperwork, then they are totally enforceable all the way to court.