2008 AMC 8 Problems/Problem 9

Problem

In $2005$ Tycoon Tammy invested $100$ dollars for two years. During the the first year her investment suffered a $15\%$ loss, but during the second year the remaining investment showed a $20\%$ gain. Over the two-year period, what was the change in Tammy's investment?

$\textbf{(A)}\ 5\%\text{ loss}\qquad \textbf{(B)}\ 2\%\text{ loss}\qquad \textbf{(C)}\ 1\%\text{ gain}\qquad \textbf{(D)}\ 2\% \text{ gain} \qquad \textbf{(E)}\ 5\%\text{ gain}$

Solution

After the $15 \%$ loss, Tammy has $100 \cdot 0.85 = 85$ dollars. After the $20 \%$ gain, she has $85 \cdot 1.2 = 102$ dollars. This is an increase in $2$ dollars from her original $100$ dollars, a $\boxed{\textbf{(D)}\ 2 \%\ \text{gain}}$ .

2008 AMC 8 (Problems • Answer Key • Resources)
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2008 AMC 8 Problems/Problem 9

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