Fill in the blank with the most appropriate word. Rakesh ……..…….  become a Bank PO by next year.

The question indicates singular, 3^rd person. Option (1) uses “will be” but does not have an -ing verb form to make in Continuous and option (3) uses “will has” which is incorrect due to two usages of helping verbs. Option (4) uses “had”  for past perfect but the reference is of a future event and not another past event as required for Past Perfect.   Option (2) satisfies the rule of Future Perfect - Subject (Shyam) + will have + verb in past participle form (become)