Original Investment $t$ Is the Time in Years $r$ Is the Annual Interest Rate Compounded Continuously, And

question 77

Multiple Choice

$\text { Suppose the capitalized cost } C \text { is given by } C = C _ { 0 } + \int _ { 0 } ^ { n } c ( t ) e ^ { - n } d t \text {, where } C _ { 0 } \text { is the }$ 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. Find the capitalized cost $C$ of an asset forever if $C _ { 0 } = 670,000 , c ( t ) = 22,000$ , and $r = 0.09$ . Round your answer to the nearest dollar.

• A) \(\$ 914,433\)
• B) \(\$ 671,980\)
• C) \(\$ 914,456\)
• D) \(\$ 914,444\)
• E) \(\$ 693,980\)

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Definitions:

Net Income

Net income is the total profit of a company after all expenses, taxes, and costs have been subtracted from total revenue.

Depreciation

The process of allocating the cost of a tangible asset over its useful life.

Net Income After Taxes

The profit a company retains after all operating expenses, interest, taxes, and preferred stock dividends have been deducted from total revenue.

Operating Costs

Operating costs are expenses associated with the maintenance and administration of a business on a day-to-day basis.