The Capitalized Cost $C$ Of an Asset Is Given By $C = C _ { 0 } + \int _ { 0 } ^ { n } C ( t ) e ^ { - r t } d t$

The capitalized cost $C$ of an asset is given by $C = C _ { 0 } + \int _ { 0 } ^ { n } C ( t ) e ^ { - r t } d t$ where $C _ { 0 }$ is the original investment, $t$ is the time in years, $r$ is the annual interest rate compounded continuously, and $C ( t )$ is the annual cost of maintenance (in dollars) . Find the capitalized cost of an asset (a) for 5 years, (b) for 10 years, and (c) forever. $C _ { 0 } = \$ 300,000 , C ( t ) = 15,000 , r = 6 \%$

A) a. For $n = 5 , C$ $\approx$ $253,901.30b. For $n = 10 , C$ $\approx$ $807,922.43c. For $n = \infty , C$ $\approx$ $4,466,666.67
B) a. For $n = 5 , C$ $\approx$ $453,901.30b. For $n = 10 , C$ $\approx$ $807,922.43c. For $n = \infty , C$ $\approx$ $1,466,666.67
C) a. For $n = 5 , C$ $\approx$ $453,901.30b. For $n = 10 , C$ $\approx$ $2807,922.43c. For $n = \infty , C$ $\approx$ $4,466,666.67
D) a. For $n = 5 , C$ $\approx$ $453,901.30b. For $n = 10 , C$ $\approx$ $807,922.43c. For $n = \infty , C$ $\approx$ $4,466,666.67
E) a. For $n = 5 , C$ $\approx$ $453,901.30b. For $n = 10 , C$ $\approx$ $807,922.43c. For $n = \infty , C$ $\approx$ $466,666.67