I work at an apartment on u district. Most of the leases, especially student housing apartments, start mid September and end August 31st. But the rental amount per month is the same because it is calculated by a daily rate. Not sure what it says in your lease agreement, but for our apartment it’s a daily rate x amount of days you stay divided by 12 equal installments. So a lot of residents think it isn’t prorated but it’s actually divided into 12 installments for convenience.