This happened to me in December. It was dec 4-jan 4th. They had to pay for New Year's Day and than I was closed the Friday, so no charge. Thankfully they never made a stink about it but if they had, I would have still charged them the same!

I charge a 1 week deposit in the beginning to be used towards the last month. If they refused to pay for that stat I would have just deducted it from the deposit and held my ground.

Good luck!!