Shall and will are modal auxiliary verbs* used to indicate a future action. These days, they are used more or less interchangeably, and it is accepted. In fact, in American English, the shall is almost irrelevant. However, when situations where you have to showcase your knowledge in Grammar arises, these things matter. You really have to know the difference, in usage, between shall and will. Here is what we have:
1. Use ‘shall’ for the first person( I, we), and ‘will’ for the third and second persons( you, he, she, it, they).
i. I [We] shall leave for Lagos tomorrow.
ii. You will leave for Lagos tomorrow.
iii. He [They] will leave for Lagos tomorrow.
2. When the speaker, however, wishes to express a strong intention or attach a sense of importance to his/her words,[so to say] prove to really mean what he is saying, the rule is reversed. That is, use ‘will’ for the first person and ‘shall’ for the second and third persons.
i. I will have them put behind bars for sure.
ii. You shall sign the papers whether you like it or not.
iii. He shall do exactly as I say.
iv. We will definitely pay.
v. They shall not be allowed to step a foot into this house.
Considering the above sentences, one can sense a strong intention or assertion behind the words. The speakers are certain of the actions. In this case, then, ‘shall’ must be used, not ‘will’.
* Modal auxiliary verbs are helping verbs used in conjuction with main verbs to express modality-ability,possibility,permission, and obligation. It is noteworthy that none of them can stand alone in a sentence without a main verb. They include: can, could, will, would, shall, should, may, might and must.