The capitalized cost, $c_1,$ of an asset over its lifetime is the total of the initial cost and the present value of all maintenance that will occur in the future. It is computed by the formula $c=c_0+{\displaystyle \underset{0}{\overset{L}{}}}m(t)e^{-rt}dt$ where $c_0$ the initial cost of the asset, $L$ is the lifetime $($in years$),r$ is the interest rate $($compounded continuously$),$ and $m(t)$ is the annual cost of maintenance. Find the capitalized cost under the following set of assumption

$c_0=$$$500,000,r=4\%,m(t)=$$$30,000,L=20$

$c=s($Round to the nearest dollar as needed.$)$