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:

Normal Rate

The standard or usual rate for a task or service, often related to wages or interest.

Cost Per Bushel

A measure of the expenses incurred to produce a bushel of an agricultural product, such as grains.

Profit

The financial gain realized when the revenue generated from a business activity exceeds the expenses, costs, and taxes needed to sustain the activity.

Total Revenue

The total amount of money a company receives from its sales of goods or services, not subtracting any costs.