What is the ruling on a teacher taking money in exchange for helping a student, given that she vowed not to give private lessons for financial compensation, but she did not refrain from helping those in need without compensation, and the student's guardian insisted on paying?

People believe that making a vow (nadhr) is a means to achieve their desired outcome, but this is incorrect. The Prophet, peace and blessings be upon him, forbade it and clarified that it does not repel anything from divine decree. It merely extracts from the miser. Scholars have unanimously agreed that it is not obligatory to fulfill a permissible vow. They only differed on whether expiation is required for it. The Hanbalis and most of the early scholars (Salaf) deemed it obligatory, while Malik and Shafi'i did not.

The correct view is that whoever makes a permissible vow, if he wishes, he may fulfill it, and if he wishes, he may abandon it, in which case he must offer expiation similar to that for a broken oath (kaffarat yameen).