Answer
$$\$17979.28$$
Work Step by Step
Given$$ R(t) =5000 e^{-0.1 t},\ \ \ \ \ \ r= 0.04 ,\ \ \ T= 5 $$
Then
\begin{align*}
\mathrm{PV}&=\int_{0}^{T} R(t) e^{-r t} d t\\
&= \int_{0}^{5} 5000 e^{-0.1 t}e^{-0.04t} d t\\
&= \int_{0}^{5} 5000 e^{-0.14 t} d t\\
&= \frac{5000}{-0.14} e^{-0.14t}\bigg|_{0}^{5}\\
&\approx \$17979.28
\end{align*}
