Later, when he finally succeeds in killing the victim, he becomes positively cheerful, feeling that he has accomplished his goal cleverly and with the rationality that he associates with sanity.
However, the unsuspecting behavior of the policemen suggests that the narrator has become essentially unaware of his behavior and his surroundings.
However, a likely logical explanation is that when the protagonist is under stress, he hears the sound of his heart, "a low, dull, quick sound, such as a watch makes enveloped in cotton," and he mistakes it for the sound of the old man's heart.
This lack of understanding parallels his lack of awareness of his actions as he chats with the policemen and highlights the lapses in reason which belie his claims of sanity.
The narrator's nerves are wracked by the sight, and he fancies that because of his oversensitivity, he has begun to hear the beating of the old man's heart.
The beating firms his resolve as he continues to increase the intensity of the light on the man's eye.By the time he finishes the clean-up, it is four in the morning, and someone knocks on the door.In a cheerful mood, the narrator answers the door only to find three policemen who have come to investigate because a neighbor heard the old man's shriek and alerted the police to the possibility of foul play.The narrator freezes, but even after an hour, the old man does not return to sleep because he feels afraid and senses someone's presence.At length, the narrator decides to slowly open the lantern until the light shines on the old man's eye, which is wide open.His unreliability becomes immediately evident in the first paragraph of the story, when he insists on his clarity of mind and attributes any signs of madness to his nervousness and oversensitivity, particularly in the area of hearing.However, as soon as he finishes his declaration of sanity, he offers an account that has a series of apparent logical gaps that can only be explained by insanity.The beating grows louder and louder until the narrator begins to worry that a neighbor will hear the noise, so he decides to attack.The old man screams once before the narrator drags him to the floor and stifles him with the mattress.In almost no cases does he respond in the manner that one would expect.He is so bothered by the old man's vulture-like eye that his loathing overcomes his love for the man, leading him to premeditate a murder.