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

question 21

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

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Definitions:

Critical Product Component

An essential part or element of a product that significantly impacts its performance or quality.

Tangible Asset

Physical assets that have a value and exist in a physical form, such as machinery, buildings, and land.

Part-time Employees

Workers who are employed for less than the standard working hours, offering flexibility and reduced workload.

In-process Inventory

Goods and materials that are partially completed in the manufacturing process but are not yet finished products.