The Narrator introduces herself/himself and describes how he/she is not a insane person. Later the narrator is describing the motive.
The narrator describes the old man's vulture like eye the key to the narrator's motive to kill the man.
The narrator stealthily creeps up to the old man's bed and checks on the old man to see if his vulture eye is open. The narrator uses a lantern to shine a little light to check if the eye is open. The narrator does this for 6 days but on the 7th day the narrator strikes
The narrator suffocates and kills the old man and chops and hides the limbs in the floorboards without a trace of blood.
The police arrive on scene and ask the narrator to search the premises. Then narrator agrees and the officers suspect nothing. They stay for a bit but the narrator is gradually becoming insane because of the ringing in his ears.
The narrator confesses because of the ringing he/she hears and can't deal with the guilt.