To determine To find: The capital value if an investment produces a perpetual stream of income with a flow rate of R ( t ) = 1200 e 0.03 t and the interest rate is 7% compounded continuously. Explanation Formula used: The capital value is C V = ∫ 0 ∞ Re − r t d t , where r is annual rate of interest 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 value of R ( t ) = 1200 e 0.03 t and r = 0.07 in the above formula and compute the capital value of the property. C V = ∫ 0 ∞ ( 1200 e 0

Calculus With Applications, Books a la Carte Plus MyLab Math Package (11th Edition)

11th Edition

ISBN: 9780133886849

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 8.4, Problem 45E

To determine

To find: The capital value if an investment produces a perpetual stream of income with a flow rate of R(t)=1200e0.03t and the interest rate is 7% compounded continuously.

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Chapter 8.4, Problem 44E

Chapter 8.4, Problem 46E

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Calculus With Applications, Books a la Carte Plus MyLab Math Package (11th Edition)

Ch. 8.1 - YOUR TURN 1 Find Ch. 8.1 - YOUR TURN 2 Find Ch. 8.1 - YOUR TURN 3 Find Ch. 8.1 - YOUR TURN 4 Find . Ch. 8.1 - YOUR TURN 5 Find Ch. 8.1 - Prob. 1WE Ch. 8.1 - Find the following. W2. Ch. 8.1 - Find the following. W3. Ch. 8.1 - Find the following. W4. Ch. 8.1 - Use integration by parts to find the integrals in...

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