Chapter 5.2, Problem 52E

The capitalized cost, c, of an asset over its lifetime is the total of the initial cost and the present value of all maintenance expenses that will occur in the future. It is computed with the formula

$c=c_0+{\displaystyle {\int }_0^{L}m\left(t\right)}{e}^{-kt}dt,$

where $c_0$ is the initial cost of the asset, L is lifetime (in years), k is the interest rate (compounded continuously), and $m\left(t\right)$

is the annual cost of maintenance. Find the capitalized cost under each set of assumptions.

How would you explain the concepts of present value and accumulated present value to a friend who has not studied this chapter?