After simple interest for two months at $5$% per annum was credited, a Boy Scout Troop had a total 
of $\textdollar 255.31$ in the Council Treasury. The interest credited was a number of dollars plus the following number of cents
$\textbf{(A) }11\qquad \textbf{(B) }12\qquad \textbf{(C) }13\qquad \textbf{(D) }21\qquad  \textbf{(E) }31$
We can use the formula $A = P(1+rt)$ for simple interest, where $P$ is the principal (initial amount), $A$ is the total, $r$ is the interest rate per year, and $t$ is the time in years.
We are solving for $P,$ so we can rearrange the equation:
\[P = \frac{A}{1+rt}\]
Plug in all the necessary numbers:
\[P = \frac{255.31}{1 + (0.05)(2/12)} = \textdollar 253.21\]
The answer is $\textbf{(D) }21$
-edited by coolmath34
If there are any mistakes, feel free to edit so that it is correct.