The problem can be represented by a geometric series with [latex]{a}_{1}=26,750[/latex]; [latex]n=5[/latex]; and [latex]r=1.016[/latex]. Substitute values for [latex]{a}_{1}[/latex], [latex]r[/latex], and [latex]n[/latex] into the formula and simplify to find the total amount earned at the end of 5 years.

[latex]\begin{align}{S}_{n}&=\frac{{a}_{1}\left(1-{r}^{n}\right)}{1-r} \\ {S}_{5}&=\frac{26\text{,}750\left(1-{1.016}^{5}\right)}{1 - 1.016}\approx 138\text{,}099.03 \end{align}[/latex]

He will have earned a total of $138,099.03 by the end of 5 years.