1971 AHSME Problems/Problem 4


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: \[P = \frac{255.31}{1 + (0.05)(2/12)} = \textdollar 253.21\] So, the interest is \[P*(0.05)(2/12) = \textdollar 2.11\]

The answer is $\textbf{(A) }11$

-edited by Happypuma46

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