Answer
$\$44,966.91$
Work Step by Step
We can compute the present value:
$\int_{0}^{T}f(t)~e^{-rt}~dt$
$= \int_{0}^{T}8000~e^{0.04t}~e^{-rt}~dt$
$= \int_{0}^{T}8000~e^{(0.04-r)t}~dt$
$= \frac{1}{0.04-r}\cdot 8000~e^{(0.04-r)t}~\vert_{0}^{T}$
$= \frac{1}{0.04-r}\cdot 8000~[e^{(0.04-r)T}- e^{(0.04-r)(0)}~]$
$= \frac{1}{0.04-0.062}\cdot 8000~[e^{(0.04-0.062)(6)}- 1~]$
$= -\frac{1}{0.022}\cdot 8000~[e^{-0.132}- 1~]$
$= \$44,966.91$
