Chapter 5.2, Problem 49E

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.

$c_0=\$400,000,k=5.5\%,m\left(t\right)=\$10,000,L=25$