The 30 days notice can be put through, you would be charged up until your contract end date though. I would hope they would not be difficult and ask you to place your notice again. As with ANY contract though, you would be expected to pay up until the final day of your contract.
As with most providers, the billing is done in advance, you may be due credit back after your contract ends though? Dependant on your current billing date and payments already made?