In "The Tell-Tale Heart," why does the narrator have a "light heart"?

Toward the end of the story, after the narrator has killed, dismembered, and hidden the body of the old man in order to rid himself of the "vulture eye," he hears a knocking at his door. Though it is only four o'clock in the morning, the narrator says, "I went down to open it with a light heart, -- for what had I now to fear?" The implication, then, is that the narrator has a light heart because he has no fear of being caught. He has already taken "wise precautions" to be sure that the body will not be discovered and that no blood was left to stain the floors (he'd thought to use a tub to catch it all when he took the old man's body apart). He feels that he has no reason to fear anyone who might be knocking at his door at this hour because he has been so careful, so meticulous, and that he has committed the perfect crime.