Answer
$\$793583$.
Work Step by Step
From the given statement, the series is $24000,1\cdot 05\left( 24000 \right),1\cdot {{05}^{2}}\left( 24000 \right),...$
From the given information, we can observe that it is a geometric series
$24000,1\cdot 05\left( 24000 \right),1\cdot {{05}^{2}}\left( 24000 \right),\cdots $
Here ${{a}_{1}}=24000$ and common ratio $r=1\cdot 05$ and $n=20$.
We use the formula for the sum of a geometric series with finite terms ${{S}_{n}}=\frac{{{a}_{1}}\left( 1-{{r}^{n}} \right)}{\left( 1-r \right)}$.
Thus
$\begin{align}
& {{S}_{n}}=\frac{24000\left( 1-1\cdot {{05}^{20}} \right)}{\left( 1-1\cdot 05 \right)} \\
& =\frac{24000\left( 1-2\cdot 653 \right)}{-\left( 0\cdot 05 \right)} \\
& =\frac{24000\left( -1\cdot 653 \right)}{-\left( 0\cdot 05 \right)} \\
& =793583
\end{align}$
