Moderate# Pie Portions

EMETRC-SB94MY

Pete receives a whole apple pie on Monday and eats half of it that evening. However, his appetite falls off after that first day. Each subsequent day, Pete will only eat $\frac{1}{4}$ of the pie that remains at the beginning of that day. If, beginning Tuesday and for each day thereafter, Pete consumes one-fourth of the remaining pie, then how much of the original pie will remain after he eats pie on Friday?