Explanation Given Information: The Gift and Card Shoppe has income stream of G ( t ) = 30000 dollars per year and Wine Boutique has income stream of W ( t ) = 21 , 600 e 0.08 t dollars per year. Formula used: According to the Present Value of a Continuous Income Stream: If t = 0 to t = k is the time interval and f ( t ) is the continuous income flow earning interest at rate compounded continuously with, then the Present Value of a Continuous Income Stream is: P V = ∫ 0 k f ( t ) e − r t d t . Calculation: Consider the income equation of Gift and Card Shoppe, G ( t ) = 30000 Since, the income to be calculated for next 12 years, So, the value of k can be determine as: k = 12 And Money is worth 10 % compounded continuously, So, the value of r can be determine as: r = 10 100 = 0.10 Considering the formula, P V = ∫ 0 k f ( t ) e − r t d t Substitute 12 for k , 0.10 for r and 30000 for f ( t ) and evaluate, P V = ∫ 0 12 30000 e − 0.10 t d t = − 300000 ∫ 0 12 e − 0.01 t ( − 0.10 ) d t = [ − 300000 e − 0.10 t ] 0 12 Solve the limit of the function, P V = [ − 300000 e − 0.10 ( 12 ) ] − [ − 300000 e − 0.10 ( 0 ) ] = 209 , 462 Therefore, the present value of Gift and Card Shoppe is $209,462

Mathematical Applications for the Management, Life, and Social Sciences

12th Edition

ISBN: 9781337625340

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Chapter 13.4, Problem 16E

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To calculate: The Present Value of the income stream for next 12 years if the money is 10% compounded continuously. Where, the Gift and Card Shoppe has income stream of G(t)=30000 dollars per year and Wine Boutique has income stream of W(t)=21,600e0.08t dollars per year. And also compare which business is better buy.

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Chapter 13.4, Problem 15E

Chapter 13.4, Problem 17E

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Mathematical Applications for the Management, Life, and Social Sciences

Ch. 13.1 - CHECKPOINT 1. For the interval [0, 2]. determine...Ch. 13.1 - Prob. 2CP Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E

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Solution Summary: The author calculates the present value of the income stream for next 12 years if the money is 10% compounded continuously.

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