Interior Design Fee

Hello, Looking an answer about the fee for an interior designer and it's scope of responsibilities. I understand basically the an interior designer once hire by a client then he/she get all the checklist from a client then from that he/she basically he/she would be able to produced design programming etc and of course he/she get paid per hour [ of course ] but I don't want to know the numbers.

Definitely he/she will get involved during the construction and face all the headache threw at him/her from the contractor.

Now my question ! How does he/she charge the fee assuming a per hour basis that he/she already spend time in DESIGN [ drawings, presentation, color, furniture , FF/E, etc]. Time during the construction period.

So, The fee = Design [say 2 weeks ] + renovation [ 6 weeks ]? Are my basic formula is right or wrong ?

Thanks,
Woodmaster