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Help the undercover secret agent complete his encrypted mission log.
By the end of this month, I _______________________________ the villain's secret password for exactly a year. Despite this success, I _________________________________ this ridiculous fake mustache for so long that I might never be able to take it off.
will have known / will have been wearing
State verbs (like know, believe, own) cannot generally be used in continuous tenses. Even though there is a duration ("for exactly a year"), we must use the Future Perfect Simple (will have known), not the continuous form.
Action verbs (like wear, run, work) can be continuous. To emphasize how long an action will have been ongoing by a future point ("by the end of this month"), we use the Future Perfect Continuous (will have been wearing).