AMC 8 2009 Problem 8

The length of a rectangle is increased by $10\%$ percent and the width is decreased by $10\%$ percent. What percent of the old area is the new area?

$\textbf{(A)}\ 90 \textbf{(B)}\ 99 \textbf{(C)}\ 100 \textbf{(D)}\ 101 \textbf{(E)}\ 110$