Explanation Formula used: The capital value is C V = ∫ 0 ∞ R e − r t d t , where r is annual rate of interest, R is the perpetual annual amount and t is time. Definition used: Improper integral: “If f is continuous on [ a , ∞ ) , then ∫ a ∞ f ( x ) d x = lim b → ∞ ∫ a b f ( x ) d x . If it exists and finite, then it is converges otherwise diverges”. Theorem used: Fundamental Theorem: “Let f be a continuous function on [ a , b ] . If F is anti-derivative of f on [ a , b ] , then ∫ a b f ( x ) d x = F ( b ) − F ( a ) ”. Calculation: Substitute the values R = $ 42 , 000 and r = 0.05 in the above formula to compute the capital value of the property. C V = ∫ 0 ∞ ( 42 , 000 ) e − 0.05 t d t = 42 , 000 lim b → ∞ ∫ 0 b e − 0.05 t d t = − 42 , 000 0.05 lim b → ∞ [ e − 0.05 t ] 0 b = − 42 , 000 5 ( 100 ) lim b → ∞ [ e − 0.05 b − e 0 ] On further simplification, C V = − 840 , 000 lim b → ∞ e − 0.05 b + lim b → ∞ ( 840 , 000 ) = − 840 , 000 lim b → ∞ e − 0

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

14th Edition

ISBN: 9780134668574

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker

Publisher: PEARSON

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Chapter 11.1, Problem 66E

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To interpret: The effect of the capital value of the property at an increased interest rate of 5% and at an decreased rate of 2% compounded continuously with an annual rent $42,000.

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Chapter 11.1, Problem 65E

Chapter 11.1, Problem 67E

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Chapter 11 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

Ch. 11.1 - Evaluate the following, if it converges: 3dx(x1)2.Ch. 11.1 - Prob. 2MP Ch. 11.1 - Prob. 3MP Ch. 11.1 - Prob. 4MP Ch. 11.1 - Prob. 5MP Ch. 11.1 - Prob. 6MP Ch. 11.1 - Prob. 1ED Ch. 11.1 - Prob. 2ED Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E

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To interpret: The effect of the capital value of the property at an increased interest rate of 5% and at an decreased rate of 2% compounded continuously with an annual rent $42,000.

Solution Summary: The author calculates the capital value of the property at an increased and decreased interest rate of 5% and 2% compounded continuously with an annual rent of 42,000.

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To interpret: The effect of the capital value of the property at an increased interest rate of 5% and at an decreased rate of 2% compounded continuously with an annual rent $42,000.

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Chapter 11 Solutions