Answer
a) $\$19,676$.
b) $\$2$.
Work Step by Step
(a)
The charges of public institutions which are given for the period of four years are 4565, 4824, 5046 and 5241 dollars.
Thus, the total costs of the public dormitory charges will be:
$\$4565+\$4824+\$5046+\$5241=\$19,676$.
(b)
Using the given model, we get,
$\begin{align}
& {{a}_{1}}=225\left( 1 \right)+4357 \\
& {{a}_{1}}=4582 \\
& {{a}_{4}}=225\left( 4 \right)+4357 \\
& {{a}_{4}}=5257
\end{align}$
So, $\begin{align}
& {{S}_{n}}=\frac{n}{2}\left( {{a}_{1}}+{{a}_{n}} \right) \\
& {{S}_{n}}=\frac{4}{2}\left( 4582+5257 \right) \\
& {{S}_{n}}=2\left( 9839 \right) \\
& {{S}_{n}}=\$19,678\end{align}$
So, the model overestimates the actual sum by $19,678-19,676=\$2$.
