Answer
$\$9$ million
Work Step by Step
From the given information, we can observe that it forms a geometric infinite series:
$6,\left( 0.6 \right)6,{{\left( 0.6 \right)}^{2}}6,\cdots $
Here ${{a}_{1}}=6$ and common ratio $r=0.6$.
We use the formula for the sum of a geometric series: ${{S}_{n}}=\frac{{{a}_{1}}}{\left( 1-r \right)}$.
Thus
$\begin{align}
& {{S}_{n}}=\frac{6}{\left( 1-0.6 \right)} \\
& =\frac{6}{\left( 0.4 \right)} \\
& =15
\end{align}$
So, the spending is
$\$15-\$6=\$9$
