Explanation Given: There is an income stream of $ 6000 a year for 10 years and the interest rate is 5 % compounded continuously. Formula Used: Present value of income S ( t ) over the time t at interest rate r % compounded continuously for M years is given as Present Value = ∫ 0 M S ( t ) e − r t d t Also, future value is given as Future Value = Present Value ⋅ e r M Calculation: Given that income stream of $ 6000 a year for 10 years and the interest rate is 5 % compounded continuously. We have S ( t ) = 6000 M = 10 r = 0.05 Present value is calculated as Present Value = ∫ 0 10 6000 e − 0.05 t d t = 6000 ∫ 0 10 e − 0.05 t d t Solve the integral using fundamental theorem of calculus and substitution method. Let − 0.05 t = u , − 0.05 d t = d u d t = d u − 0.05 Also, when t = 0 , u = 0 When t = 10 , t = − 0.5 Present Value = 6000 ∫ 0 − 0 To determine (b) To find the how much of the future value is from income stream and how much is from interest.

6th Edition

ISBN: 9781119267874

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 6.5, Problem 9P

To determine

(a)

To find the present and future value.

To determine

(b)

To find the how much of the future value is from income stream and how much is from interest.

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Chapter 6.5, Problem 8P

Chapter 6.5, Problem 10P

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(a) To find the present and future value.

Solution Summary: The author calculates the present and future value of income using the fundamental theorem of calculus and substitution method.