1981 AHSME Problems/Problem 13

Problem

Suppose that at the end of any year, a unit of money has lost 10% of the value it had at the beginning of that year. Find the smallest integer $n$ such that after $n$ years, the money will have lost at least $90%$ (Error compiling LaTeX. Unknown error_msg) of its value (To the nearest thousandth $log_{10}^{3}=0.466$ ).

$\textbf{(A)}\ 14\qquad\textbf{(B)}\ 16\qquad\textbf{(C)}\ 18\qquad\textbf{(D)}\ 20\qquad\textbf{(E)}\ 22$

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1981 AHSME Problems/Problem 13

Problem