Find the Capitalized Cost C of an Asset Forever $C = C _ { 0 } + \int _ { 0 } ^ { n } c ( t ) e ^ { - r t } d t$

Multiple Choice

Find the capitalized cost C of an asset forever. The capitalized cost is given by $C = C _ { 0 } + \int _ { 0 } ^ { n } c ( t ) e ^ { - r t } d t$ where $C _ { 0 } = \$ 500,000$ is the original investment, t is the time in years, r = 12% is the annual interest rate compounded continuously, n is the total time in years over which the asset is capitalized, and $c ( t ) = 25,000 ( 1 + 0.08 t )$ is the annual cost of maintenance (measured in dollars) . Round your answer to two decimal places.

A) $1,125,000.00
B) $875,000.00
C) $708,333.33
D) $899,218.75
E) $847,222.22