Explanation Given information: The rate of earnings is 50 + 7 t thousand dollars per year at time t and the interest rate is 10 % . Formula used: Present value of a continuous stream of income: [ present value ] = ∫ T 1 T 2 K ( t ) e − r t d t , where K ( t ) is the annual rate of income at time t , r is the annual interest rate and T 1 to T 2 (years) is the time period of the income stream. Integration by parts rule: ∫ f ( x ) g ( x ) = f ( x ) G ( x ) − ∫ f ' ( x ) G ( x ) d x , where G(x)= ∫ g(x) dx and f ′ (x) is the derivative of f ( x ) . Calculation: Substitute the values K ( t ) = 50 + 70 t , r = 10 % , T 1 = 0 , and T 2 = 2 in the above formula. Present value = ∫ 0 2 ( 50 + 7 t ) e − 0.1 t d t Let f(t)=50+7t , g(t)=e -0 .1t dt , then f ′ (t)=7 and G(t)= ∫ e -0 .1t d t = − e -0 .1t 0.1 By using the integration by parts rule, ∫ 0 2 ( 50 + 7 t ) e − 0.1 t d t = ( 50 + 7 t ) ( e − 0.1 t − 0.1 ) | 0 2 − ∫ 0 2 7 ( e − 0

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 9.5, Problem 8E

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To calculate: The present value of the stream of earnings generated over the next 2 years, when the rate of earning is 50+7t thousand dollars per year at time t and the interest rate is 10%.

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Chapter 9.5, Problem 7E

Chapter 9.5, Problem 9E

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The present value of the stream of earnings generated over the next 2 years, when the rate of earning is 50 + 7 t thousand dollars per year at time t and the interest rate is 10 % .

Solution Summary: The author calculates the present value of a stream of earnings generated over the next 2 years, when the rate of earning is 50+7t thousand dollars per year.

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To calculate: The present value of the stream of earnings generated over the next 2 years, when the rate of earning is 50+7t thousand dollars per year at time t and the interest rate is 10%.

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Chapter 9 Solutions