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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Definitions:

Level Of Satisfaction

A measure of how goods, services, or conditions meet an individual's needs, desires, or expectations.

Risk Averse

A description of an individual or entity that prefers to avoid risk or chooses lower risk options when faced with uncertainty, often prioritizing security over potential higher returns.

Utility Function

A mathematical representation describing how consumers rank different bundles of goods based on the level of satisfaction they provide.

Marginal Utility

The extra pleasure or benefit derived from the consumption or utilization of an additional unit of a product or service.