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

question 16

Multiple Choice

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

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