Prorating a month to month lease
I am a landlord in New Jersey, I rented my apartment for a year then it turned into a month to month lease, the tenant told me about three months ago that he would initially be leaving in June but since he was looking to buy a house and it took longer than expected it turns out he will be leaving in August, there was only verbal communication as to the move out dates and we both agreed we would be flexible with each other. My question is this. His rent is due the 24th of each month, he has paid the full months rent to August 24th but is moving out on August 15th am I obligated to give him back the remaining days from the 15th to the 24th?
Thank you for your time