The narrator himself gives the reason why he only killed the old man on the eighth night. He had been visiting his room at midnight for seven nights in a row expecting to see the old man's wasted eye open. The eye, "the eye of a vulture -- a pale blue eye with a film over it," had become an obsession with the narrator for, from the first time he had seen it, it made his blood turn cold. The eye horrified him and he decided to kill the old man and thus rid himself of having to see the horrible eye ever again, as he states,
I made up my mind to take the life of the old man, and thus rid myself of the eye forever.
During each of the seven visits, when the narrator shone a light upon the eye, he found it closed and thus relented from completing his insidious task. He obviously wanted the eye to be open before he proceeded. In his crazed state, the narrator clearly believed that the eye being open would be a signal for him to do his evil.
On the eighth night of the storyteller's surreptitious visit, he felt invigorated and proud of his intelligence and judgment. When he later shone the light on the sleeping man's eye, he found that it was open -- the sign that he had been waiting for for so long. He hesitated for a minute but then, disturbed by the sound of the old man's beating heart growing louder, went into a frenzy, jumped into the room, dragged the old man from his bed and pulled his heavy bed over him. The old man, clearly too frail and weak to push off the heavy object, suffocated and died.
The number eight in the story also has symbolic significance: in Christian culture, it is seen as the number for regeneration and new beginnings. It is evident that the narrator believed being rid of the old man and, therefore, his terrible eye, would mean a new beginning for him -- a life without the horror of being exposed to the old man's evil eye.