Explanation Given: The perpetual annual rent is $2,400 with an interest rate 6% compounded continuously. Formula used: The capital value is given by C V = ∫ 0 ∞ R e − r t d t , where R is perpetual annual rent, r is annual rate of interest and t is the time period. Definition used: Improper integral: If f is continuous on [ a , ∞ ) , then ∫ a ∞ f ( x ) d x = lim b → ∞ ∫ a b f ( x ) d x . The improper integral converges if the limit exists; otherwise diverges. Theorem used: Fundamental Theorem: Let f be a continuous function on [ a , b ] . If F is the anti-derivative of f on [ a , b ] , then ∫ a b f ( x ) d x = F ( b ) − F ( a ) . Calculation: Substitute the values R = $ 2 , 400 and r = 0.06 in the formula of capital value. C V = ∫ 0 ∞ ( 2 , 400 ) e − 0.06 t d t = 2 , 400 lim b → ∞ ∫ 0 b e − 0.06 t d t = − 2 , 400 0

14th Edition

ISBN: 9780135961407

Author: Barnett

Publisher: PEARSON CO

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Chapter 11, Problem 39RE

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To find: The capital value of the property at 6% compounded continuously.

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Chapter 11, Problem 38RE

Chapter 11, Problem 40RE

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Chapter 11 Solutions

EP CALCULUS F/BUS.,ECON.-BRIEF-ACCESS

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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The capital value of the property at 6% compounded continuously.

Solution Summary: The author calculates the capital value of the property at 6% compounded continuously.

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