Why are we suggesting euthanasia before suggesting things that might help them pay for the vet trip? A vet wouldn't put that rat down anyway just for a broken tail.
Please look into Care Credit. It is basically a credit card that you only use for health related things and they allow you to use it for vets as well. You'd have to find a vet that takes it, which may be harder. Also, explain your situation to a vet and I can almost guarantee they'll work with you on a payment plan. From the look of the tail, it only needs to be reset and taped up. Unfortunately, they'll probably have to do anesthesia to reset it (since I guarantee an awake rat wouldn't appreciate it), which might be a little expensive, but not too much. You do need to do something about it though.