Step 1: First order elimination means the remaining quantity is halved with every passing half life, a simple geometric decay.
Step 2: Compute the leftover fraction after $n=4$ half lives using $$\text{fraction remaining} = \left(\frac{1}{2}\right)^{4} = \frac{1}{16} = 6.25\%.$$
Step 3: The fraction cleared is the complement, $100\% - 6.25\% = 93.75\%$, matching the option closest to 93 percent.
\[\boxed{93\%}\]