Chapter 5.2, Problem 50E

To determine

To calculate: The capitalized cost $c$ of the assets of its lifetime where it is provided that the it is the total of the initial cost and the present value of all the maintenance expenses in future.

Capitalized cost computed with the formula, $c=c_0+{\displaystyle \underset{0}{\overset{L}{\int }}m\left(t\right)e^{-kt}dt}$, where $c_0$ is the initial cost of the asset, $L$ is the lifetime (in years), $k$ is the interest rate (compounded continuously), and $m\left(t\right)$ is the annual cost of maintenance.

$c_0=\$600,000$, $k=4\%$, $m\left(t\right)=\$40,000+\$1000e^{0.01t}$, $L=40$