Final answer:
The sentence contains a compound verb 'will have been,' which is in the future perfect tense, indicating an action that will be completed before a specified future time.
Step-by-step explanation:
The sentence “On Friday, it will have been exactly three weeks since my daughter was born” does contain a compound verb. A compound verb consists of two or more verbs that are joined by a conjunction and share the same subject. In this sentence, the verbs are “will have been” and the shared subject is “[it]”. This compound verb is in the future perfect tense, which is used to describe an action that will be completed before a specified point in the future.