Ana's monthly salary was $$2000$ in May.  In June she received a 20% raise.  In July she received a 20% pay cut.  After the two changes in June and July, Ana's monthly salary was
$\text{(A)}\ 1920\text{ dollars} \qquad \text{(B)}\ 1980\text{ dollars} \qquad \text{(C)}\ 2000\text{ dollars} \qquad \text{(D)}\ 2020\text{ dollars} \qquad \text{(E)}\ 2040\text{ dollars}$
Notice that a 20% raise translates to Ana's monthly salary multiplied by $(100 + 10)\% = 120\%$, and a 20% pay cut translates to her salary multiplied by $100\% - 20\% = 80\%$, so

\[2000 \cdot 120\% = 2400\]
\[2400 \cdot 80\% = 1920 \rightarrow \boxed{\textbf{A}}\]