Isn't it illegal to charge monthly rent for your pet? The damage deposit is understandable, but I've heard that charging rent for a pet is illegal because pets don't have jobs...
The breed thing annoyed me as well.
Things like this make me wish I was rich enough to afford a whole bunch of houses -- I would rent them out to people with animals. Over here it's practically impossible to find a house that allows pets. You have to buy the house. And apartments either ban all dogs, or dogs over a certain height. I'm really hoping that someone I know will buy a house and allow me to rent it out. I don't know what I'd do if I couldn't find a house to rent.
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