This can also be used for the present habitual. I work on Saturday is accepted but I work on Saturdays isn't accepted. As it is habitual, Saturdays should be accepted as this implies Saturdays in general. I would argue that Saturday should not be accepted in the present habitual as it implies a single or specific Saturday.
I agree with the first respondent above. I have been marked wrong for using 'I shall' etc, when it had been marked correct in an earlier question, I think twice. It's simple: I shall/ you will/ they will/ we shall/ you will/they will. This reverses only as an intensifier: "One day, Scotland shall be free!"
This article from Wikipedia provides an interesting history: https://en.wikipedia.org/wiki/Shall_and_will#Prescriptivist_distinction.
Broadly speaking, I agree with with the statement "...shall is used with the meaning of obligation, and will with the meaning of desire or intention."