Question about using future in the past

Question

Are both of these sentences correct?

They hoped that he would finish his book by the end of the month.
They hoped that he would have finished his book by the end of the month.

I think that the first one is correct, but my teacher said that the secod one is correct. I do not understand why this is the case.

Answer 1

They are both fully grammatical and fully idiomatic, and refer to exactly the same objective circumstances.

The difference, as is usual in the case of a perfect form, is entirely in how the speaker is choosing to present the temporal structure of what they are saying.

In They hoped that he would finish his book by the end of the month, they are looking forward from when they were hoping.

In They hoped that he would have finished his book by the end of the month, they are imagining themselves looking backward from the end of the month.

In this case, there is very little difference in meaning; sometimes the choice sets up an expectation about the time of following sentences.

Edit: Books4languages has suggested an alternative interpreation of the second, as a counter-factual conditional (implying that he didn't finish by the end of the month). I agree that this is a possible reading, but it is not the meaning that occurred to me.

Answer 2

Yes, both of these sentences are grammatically correct. You are using "would" in two different ways here:

"Would finish": would for future in the past

When talking about the past we can use would to express something that has not happened at the time we are talking about:

• He left 5 minutes late, unaware that the delay would save his life.
• We knew he would find somewhere to stay, regardless of not having any money; he would stay with a friend in the area.

"Would have finished": would for conditionals

We often use would to express the so-called second and third conditionals:

• If he had not left 5 minutes late, the delay would not have saved his life.
• He would have found somewhere to stay, regardless of not having any money; he would have stayed with a friend in the area.

As we can see, these sentences are in the past tense and convey the same information.