Comment Your post is the scenario the 5th protects against (Score 1) 768
"Have you stopped beating your wife yet? I insist that you answer yes or no!"
When the questioner gets to set not only the question but the range of acceptable answers -- just as you have tried to do here -- the right to remain silent is vital.
For the government to convict you of lying about not committing the murder, they would also have to convict you of the murder, and if they can convict you of murder, then you're already screwed anyway, regardless of whether they also convict you of lying about being innocent.
The penalty for murder is greater than the penalty for perjury, yes; but that's not true for all crimes. "Making false statements" was part of Martha Stewart's conviction. And cops will lead you into false statements, that's their job. If you can watch this video and not understand the importance of the Fifth Amendment, you're hopeless.