Answer
Salary paid in the sixth year is $\$42,823$ and the total salary paid over the period of six years is $\$223,210$.
Work Step by Step
Let us assume the starting salary is $a_1$ and $d$ is the raise in salary every year.
Therefore,
${{a}_{1}}=32000,r=1.06$
And the salary for 6 years is thus:
$\begin{align}
& {{a}_{1}}=32,000,\ r=1.06 \\
& {{a}_{n}}={{a}_{1}}{{\left( r \right)}^{n-1}} \\
& {{a}_{6}}=32,000{{\left( 1.06 \right)}^{5}} \\
& {{a}_{6}}\approx \$42,823\\\end{align}$
Therefore, the total salary over a six-year period can be calculated as given below:
${{S}_{n}}=\frac{{{a}_{1}}\left( 1-{{r}^{n}} \right)}{1-r}$
$\begin{align}
& {{S}_{6}}=\frac{32,000\left( 1-{{\left( 1.06 \right)}^{6}} \right)}{1-1.06} \\
& \approx \$223,210\end{align}$
