Using "will" in a sentence vs not using "will"

Question

I'm an ESL teacher. A student asked me a question regarding this sentence.
"Don't phone Ann now. She'll be busy." The student asked me why we have to use "will" in the sentence. Why shouldn't the sentence just be: "Don't phone Ann now. She's busy." I told her sentence one is predicting what is and the second is reporting what is, but I feel like I short changed my student. Perhaps there's a more detailed explanation someone might have?

Answer 1

Will is a modal auxiliary verb, and, like all the English modal auxiliary verbs

can, could, shall, should, may, might, will, would, must, and sometimes need and dare

will has two senses, called its deontic /de'yantɪk/ and its epistemic /ɛpə'stɛmɪk/ senses:
(Sorry; I don't make up these names, honest. They're standard in the literature.)

1. The deontic sense of will means that the subject is willing to do something.
   This is the only sense of will that occurs in hypothetical clauses with if, for instance.
   E.g, If he will hand in the homework, I will grade it means 'if he is willing to do it',
   with an invited inference that he has previously refused to do it. The will in the second clause can either be deontic (I am willing to correct it) or an epistemic prediction.

2. The epistemic sense of will means the speaker's personal judgement of
   (in this case) the subject's probability of being busy at some time in the future.
   This is the sense of will that is often called "the future tense" in Latinate grammar textbooks.

It is the case, however, that all modal auxiliary verbs can, and usually do, refer to the future;
since there is no future inflectional tense in English, modals are often used for the purpose,
and are often arrayed to express differences in the provenance of the judgement.

Though I have always wondered how will (and occasionally shall, though not in America)
got singled out for accolade of "Future Tense", ignoring all the other modals.
My best theory so far is that it's because epistemic will has so little other meaning,
and because it makes a nice contrast with the other future tense, going to.

As pointed out in the other answers, in this context, in this sentence

Don't phone Ann now; she'll be busy.

the use of she'll be, instead of she's, expresses the speaker's best guess,
whereas the use of she's expresses the speaker's certainty.

And other modals could express other modalities, using the same structure --
many of them are ambiguous between epistemic and deontic senses:

• Don't phone Ann now; she could be busy.
• Don't phone Ann now; she should be busy.
• Don't phone Ann now; she may be busy.
• Don't phone Ann now; she might be busy.
• Don't phone Ann now; she will be busy.
• Don't phone Ann now; she would be busy.
• Don't phone Ann now; she must be busy.

(I ignore periphrastic modals like hafta, gotta, oughta, etc. here. Life is short.)

Answer 2

There are pragmatic implications beyond the obvious.

"Don't phone Ann now. She's busy."

This is a statement of a known existing state (eg I know she's got three essays to complete in the next four days, or when I left her 30 minutes ago she had to pick her two kids up, feed them and get them to the Scouts).

"Don't phone Ann now. She'll be busy."

This is a statement of a very probable state, though the probability factor is less than the certainty expressed in the alternative. She may have three essays to complete in the next ten days, say. She needs time, though perhaps at this instant she's just having tea.