First and foremost, the murder is premeditated. The narrator visits the old man's bedroom nightly simply to stare at him as he sleeps. On the occasion that the man awakes, the narrator tortures him by standing still, noiseless, while the old man lies petrified listening for any hint that someone is in his room. The narrator is obsessed with the old man's eye..."that hideous eye!" It seems it is the eye that compels the narrator to murder the old man in cold blood. During and immediately after the murder, the narrator has the awareness that the noise may have been heard by the neighbors, so he hastily seeks the "perfect" hiding place for the evidence of his crime--under the floor boards of the bedroom.
The narrator calmly entertains the police and boldly places them directly over the hiding place of the man's remains. It is his guilt and the noise of the heartbeat which he perceives grows louder with each passing minute of the interview that is the bane of his existence. Unable to take it anymore, he confesses his crime by tearing up the floorboards before the police.
His actions, his erratic thought process, the periods of lucidity and madness should be enough to prove his unstable mental health.
The narrator is indeed mad, which also makes him an unreliable narrator. We know he is mad because he has no real reason to murder the old, defenseless man other than the fact that he has a peculiar eye. The palish-blue eye taunts and irks the narrator to the point of insanity. The man decides to murder the bearer of the eye but cannot do so when his eyes are closed. The insane narrator rationalizes that his crime must be committed when the eye is in view because he is in fact antagonized by the eye and not by the old man. This rationalization, although perfectly normal to the story teller, makes no sense to a sane person.
For eight nights, the madman stalks his victim as he meticulously plans his crime. Ironically, this carefulness to him is a sign of his sanity, and he assures the reader that no madman would be able to be so keen. However, the reader sees the man's reasoning of the ploy as utterly lunatic, and we watch the narrator on his path through madness.
Once the murder has been committed, the narrator demonstrates his insanity once again by imagining the sound of the victim's heart. It beats louder and louder until he finally confesses.