The Capital Value of an Asset Such as a Machine $\int_{0}^{\infty} K(t) e^{-r t} d t$

question 97

Short Answer

The capital value of an asset such as a machine is sometimes defined as the present value of all future net earnings of the asset.The actual lifetime of the asset may not be known, and since some assets last indefinitely, the capital value of the asset may be written in the form $\int_{0}^{\infty} K(t) e^{-r t} d t$ ,
where K(t)is the annual rate of earnings produced by the asset at time t, and r is the annual interest rate, compounded continuously.Find the capital value of an asset that generates income at a rate of $1000 per year, with an interest rate of 9%.Round to the nearest dollar.

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Definitions:

Smooth ER

A type of endoplasmic reticulum in cells, lacking ribosomes, involved in lipid synthesis, detoxification, and calcium ion storage.

Cholesterol

A waxy, fat-like substance found in all cells of the body, necessary for the production of hormones, vitamin D, and bile acids.

Basal Body

Structure involved in the organization and anchorage of a cilium or flagellum. Structurally similar to a centriole; each is in the form of a cylinder composed of nine triplets of microtubules (9 × 3 structure).

Flagellum

A long, whiplike structure extending from certain cells and used in locomotion. (1) Eukaryote flagella consist of two central, single microtubules surrounded by nine double microtubules (9 + 2 structure), all covered by a plasma membrane. (2) Bacterial flagella are filaments rotated by special structures located in the plasma membrane and cell wall. (3) Archaea have a rotating appendage, an archaellum, for motility.