The narrator actually likes the old man. He says in the second paragraph of the story that he had nothing against the old man. This was not a crime of passion or one of insult. In fact, he says,
"I loved the old man." (page 1, paragraph 2)
Then he says,
"I think it was his eye! -----yes, it was this! He had the eye of a vulture ---- a pale,blue eye, with a film over it. Whenever it fell upon me, my blood ran cold; and so, by degrees --- very gradually ---- I made up my mind to take the life of the old man, and thus rid myself of the eye forever!" ( paragraph 2)
This reasoning, this logic, is what signals for the reader that the man really is insane. Poe even plants the seed in the reader's mind when in the first paragraph he says
".....but why will you say that I am mad?" ( paragraph 1)
After he kills the old man, the narrator brags about how clever he was in concealing the old man's body.
"First of all, I dismembered the corpse. I cut off the head and the arms and the legs. I then took up three planks from the flooring of the chamber, and deposited all between the scantliings. I then replaced the boards so cleverly, so cunningly, that no human eye ----not even his --- could have detected anything wrong." (paragraph 12) There was........no bloodspot whatever. ...A tub had caught all ---ha! ha!
In other words, he cut the body up in a tub so that blood wouldn't go anywhere. He cut off the head, the arms, and the legs. He then pulled up three boards from the floor in the bedroom and put the body parts in the structure of the bedroom. He then cleverly put the boards back and was really impressed with his work. He said no one would ever be able to tell that anything was below the boards.