Answer: If your analogy is right, then it means that paying a worker by the hour or by the day also supposed to be interest. But this is not the case.

In every job, work is done within a certain amount of time. However, it is not the norm that people charge for the time they have used, instead, they charge for the work which has been done. In the same context, teaching is a job which is done by an individual, when he accepts a wage for teaching, he is doing so for a task/job which he has performed and not a time. If we use your assumption it means that no Muslim would be able to be a teacher at any Institution whether Islamic or otherwise.

As far as Interest is concerned, it is of two types, namely Riba An Nasee'a and Riba Al Fadhl. If you need to know more about the concept and rulings regarding Interest, you can let us know.

And Allah knows best.
Mufti Waseem Khan