Explanation Given: There is an income stream of $ 12000 a year for 20 years. The interest rate is 6 % 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 $ 12000 a year for 20 years and interest rate is 6 % compounded continuously. We have S ( t ) = 12000 M = 20 r = 0.06 Present value is calculated as Present Value = ∫ 0 20 12000 e − 0.06 t d t = 12000 ∫ 0 20 e − 0.06 t d t Solve the integral using fundamental theorem of calculus and substitution method. Let − 0.06 t = u , − 0.06 d t = d u d t = d u − 0.06 Also, when t = 0 , u = 0 When t = 20 , u = − 1.2 Present Value = 12000 ∫ 0 − 1

6th Edition

ISBN: 9781119267874

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 6.5, Problem 2P

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Find the present and future value of an income stream of $12000 a year for 20 years. The interest rate is 6% compounded continuously.

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Chapter 6.5, Problem 1P

Chapter 6.5, Problem 3P

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Find the present and future value of an income stream of $ 12000 a year for 20 years. The interest rate is 6 % compounded continuously.

Solution Summary: The author calculates the present and future value of an income stream of 12000 a year for 20 years.

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Find the present and future value of an income stream of $12000 a year for 20 years. The interest rate is 6% compounded continuously.

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Chapter 6 Solutions