Rent weekly cost database design
You need to have a rentals table which has the following minimum columns:


id - unique identifier for the rental an autoincrement field 
roomid - FK to the id of the room
startdate and enddate - of the rental 
weekcoefficient - computed from either the startdate or enddate to be enable a lookup to week coefficient cost table (while its not adviseable to store computed columns, this may be necessary for performance reasons) 
buildingid (optional) - FK to the id of the building (allows a direct lookup from the rental to the building without having to go through room table for performance reasons) 
categoryid (optional) - similar explanation to the buildingid above to lookup the category coefficient table. This column may also be useful later in case the categories of the building change over time as it tracks the historical record for the category of the building at the time of allocation 


UPDATE: To cater for the computation of the room coefficients with dependence on the building in which the room is located

To compute the different room coefficients you can have either:


a table with 3 columns: a number corresponding to output from WEEKOFYEAR function on a specific date, buildingid,  the coefficient (will have 52 values x the number of buildings) 
Write a stored function which takes a date and matches the coefficient if there are few values specified by a range or if the combinations have some logic to them based on other features or data (any more than 10 different combinations makes this a nightmare)


Either approach above will require you to save the coefficient in the rentals table for historical reporting/auditing purposes and also maintain a note on what data was used for computation at that time