Must doesn’t change its form, whatever be its tense or the number and person of its subject. It can refer to the present or future. You must do this now. (Present) He must pay damages. (Future) You must file a petition. (Future)
Would is the past tense of will in indirect speech. Direct: The manager said, ‘The shop will be closed on Monday.’ Indirect: The manager said that the shop would be closed on Monday. >>> Read More.
With the first person The modal auxiliary verb shall is used with first person pronouns to express the strong possibility or near certainty of an action which is to take place in the near future.>>> Read More.