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Throughout their school life, children will have listened to many stories being read to them.

Please explain the use of the tense "will have listened...

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It has the form of future perfect tense, but most probably it is not a literal temporal use, but is intended to express the speaker's belief/assumption about the general experience of children.

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You need to be careful here about distinguishing grammatical tense and meaning.

Ignoring the "being read" clause, syntactically there are three clauses, as bracketed:

Throughout their school life, [children will [have [listened to many stories being read to them]]].

"Will" is a present tense modal verb, so the overall (matrix) tense of the sentence is present. Embedded in the matrix clause, the clause "have listened to many stories being read to them" is the perfect tense (i.e. a past tense), and finally "listened to many stories being read to them" is a past-participial clause as complement of the perfect auxiliary "have".

Semantically, the modal meaning of "will" is epistemic here, i.e. 'what is possible' given our present knowledge. It has a past time meaning here, though the perfect is used to express current relevance.