Hello!
Correct answer is A: will have finished.
The future perfect is used when talking about an action that will be finished before another action in the future. By this time next week (1st clause), we WILL HAVE FINISHED (already) our finals exam. Its structure: WILL HAVE + PAST PARTICIPLE OF THE VERB
Had finished is past perfect, and it is used to talk about something that occurred before another action in the past.
Will finish could also work, but you were asked for the future perfect and will is future simple.
Finally, have finished does not work. 1. This is present perfect. 2. Present perfect is used
Hope this helps.
