I'm going to go to the gym now, and by the time I come back, the room will have been cleaned by the housekeeper.
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pathfinder1992The best modal to use is would, because of the past tense of have beenActually, would would be wrong. Will is needed to locate the situation in future time, with have been emphasizing completion. The presence of the present perfect does not require the past form of the modal in this case.
pathfinder1992 It is a counterfactual situation;It isn't.
pathfinder1992 you can never be sure whether the room will be cleaned or notWe can never be 100% sure of the factuality of any future situation. However, the use of the modal 'will' indicates the speaker's certainty.The future cleaning of the room is,