The narrator of "The Tell-Tale Heart" is crazy; however, he repeatedly tries to tell readers that he is completely sane:
How, then, am I mad? Hearken! and observe how healthily—how calmly I can tell you the whole story.
Unfortunately other things that the narrator says absolutely alert readers to the fact that the narrator is insane. He believes that his master must die because he has a creepy eye:
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.
The narrator also claims that he has super hearing that allows him to hear things from hell:
I heard all things in the heaven and in the earth. I heard many things in hell.
Despite the fact that the narrator is not clearly thinking about the value of life, he is very careful about his plan to kill the old man and get away with the deed. First of all the narrator is patient. He waits a week before killing the man. During that time the narrator scopes out the old man's sleeping habits. Each morning the narrator then tries to subtly figure out if the old man has noticed being spied upon:
And this I did for seven long nights—every night just at midnight—but I found the eye always closed; and so it was impossible to do the work; for it was not the old man who vexed me, but his Evil Eye. And every morning, when the day broke, I went boldly into the chamber, and spoke courageously to him, calling him by name in a hearty tone, and inquiring how he has passed the night. So you see he would have been a very profound old man, indeed, to suspect that every night, just at twelve, I looked in upon him while he slept.
After the murder is completed the narrator continues to be extremely cautious. He disposes of the body in a methodical and planned out way. He is conscious of the fact that he needs to leave no blood evidence, and that is why he chooses to dismember the body in the bathtub:
I then replaced the boards so cleverly, so cunningly, that no human eye—not even his—could have detected any thing wrong. There was nothing to wash out—no stain of any kind—no blood-spot whatever. I had been too wary for that. A tub had caught all—ha! ha!
When the police show up, the narrator has an explanation ready for why his master is not home:
The shriek, I said, was my own in a dream. The old man, I mentioned, was absent in the country.
All in all the narrator was exceptionally careful about his planning before the murder and his actions to cover it up. If I had to pick one thing that was not as carefully planned out and executed, it would be the narrator's actual moment of the killing. That is when his emotional hatred of the eye overpowers his careful logic. He lets out a yell, illuminates the room, and gives the old man the opportunity to scream:
With a loud yell, I threw open the lantern and leaped into the room. He shrieked once—once only.
Those noises were heard by a nearby neighbor that alerted the police. It is possible that the narrator would have eventually confessed his crime anyway, but he would not have confessed that night had there been no officers present to search the house and confess to.
The madness of the narrator in "The Tell-Tale Heart" prohibits him from thinking rationally, and it is obvious that there is no justification in killing a man because he has an evil eye--a "vulture eye." Further, he admits that he loves the man and that he has no intention of stealing his money. The narrator is careful about taking precautions to keep the old man from uncovering his plot to kill him, however. He "was never kinder" to the old man in the days before he planned to kill him, and he slowly and "oh so gently!" opened the door each night, taking an hour to place his head inside the room. But for seven nights, he could not kill the old man: The eye was always open. On the eighth night, he took similar precautions, but his chuckling may have alerted the old man; his slip of the latch awakened him. These noises caused the man to open the eye, and it gave the narrator the excuse to finally fulfill his goal.