Rental "month" is considered to be actual calendar days in the period for which rent is paid unlike a hotel where you pay a daily rate which means you pay less in Feb than in December. Hence in Feb which has 28 days and March which has 31 days you pay the same $490 as in Sept which has 30 days. When you give notice to vacate at the natural end of your rental month, be it 15th to 14th of the next period or 1st- 30th etc. the rent is the same. The only time a landlord pro rates using a daily rate is for example a tenant says I need an extra 7 days to get my stuff out. Some landlords arrive at the daily rate using the actual number of days in the particular month and some use the older banking convention of dividing rent by 30 days and multiply the resulting daily rate, $16.33/day in your case, by 7 days in my example. Usually the daily prorate is stated in the rental agreement, at least I include it so there is no question. So to get your rental period in sync with the calendar month your pro rate is $245 and for Sept 1 - 30 you will pay $490 and Oct 1-31 you pay $490.

The other answers are correct that you owe $245.

But, for your own knowledge, pro-rating rent is a simple calculation. Basically, you figure out the rental amount per day and then multiple it by the number of days you owe:

daily rent = monthly rent / number of days in month

Prorated rent owed = daily rent * number of days owed.

I read your comment & yes, you are correct. $245 is the amount you need to pay on Sept 1st for Sept's rent because you paid your rent through Sept 15th on Aug 15th. You already paid for half the rent for the month of Sept. You owe the other half.

Exactly half since you owe 15 days out of a 30 day month.