Explanation Given information: The capital value of an asset such as a machine is defined as the present value of the future net earnings. This asset generates income at the rate of $ 5000 per year, assuming an interest of 10 % which is compounded continuously. Formula used: The actual lifetime of the asset may not be known and since some assets may last indefinitely, the capital value of the asset may be written in the form [ c a p i t a l v a l u e ] = ∫ 0 ∞ K ( t ) e − r t d t where r is the rate of interest compounded continuously. Calculation: In this case K ( t ) = $ 5000 , r = 10 % = 0.1 . By using the capital value formula, c a p i t a l v a l u e = ∫ 0 ∞ 5000 e − 0.1 t d t This is an improper integral and apply the definition below to solve that integral. Let a be fixed and suppose that f ( x ) is a nonnegative function for x ≥ a and if lim b → ∞ ∫ a b f ( x ) d x = L , then ∫ a ∞ f ( x ) d x = lim b → ∞ ∫ a b f ( x ) d x = L

Calculus & Its Applications (14th Edition)

14th Edition

ISBN: 9780134437774

Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar

Publisher: PEARSON

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Chapter 9.6, Problem 48E

To determine

To calculate: The capital value of an asset such as a machine which is defined as the present

value of the future net earnings which generates income at the rate of $5000 per year, assuming

an interest of 10% that is compounded continuously.

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Chapter 9.6, Problem 47E

Chapter 9.6, Problem 49E

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Chapter 9 Solutions

Calculus & Its Applications (14th Edition)

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The capital value of an asset such as a machine which is defined as the present value of the future net earnings which generates income at the rate of $ 5000 per year, assuming an interest of 10 % that is compounded continuously.

Solution Summary: The author calculates the capital value of an asset such as a machine, which generates income at the rate of 5000 per year.

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To calculate: The capital value of an asset such as a machine which is defined as the present

value of the future net earnings which generates income at the rate of $5000 per year, assuming

an interest of 10% that is compounded continuously.

Want to see the full answer?

Chapter 9 Solutions

The capital value of an asset such as a machine which is defined as the present value of the future net earnings which generates income at the rate of $ 5000 per year, assuming an interest of 10 % that is compounded continuously.

Solution Summary: The author calculates the capital value of an asset such as a machine, which generates income at the rate of 5000 per year.

Concept explainers

Videos

To calculate: The capital value of an asset such as a machine which is defined as the present value of the future net earnings which generates income at the rate of $5000 per year, assuming an interest of 10% that is compounded continuously.

Want to see the full answer?

Chapter 9 Solutions

To calculate: The capital value of an asset such as a machine which is defined as the present

value of the future net earnings which generates income at the rate of $5000 per year, assuming

an interest of 10% that is compounded continuously.