How do I calculate my first rent?

If the beginning of my booking is between the 1^st and 14th of the month, I will only pay the rent of the first month. 

If the beginning of my booking is after the 15th of the month, I will pay the rent of the remaining days of the first month & rent of the following month. 

For example, if I booked my room from the 3^rd of September, my first rent will be the rent from 3rd until the end of September. 

If I book my room on the 20^th of August, my first rent will be the rent from 20^th until end of August + full rent of September.