Explanation Given: There is an income stream of $ 2000 a year for 15 years and 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 $ 2000 a year for 15 years and interest rate is 5 % compounded continuously We have S ( t ) = 2000 M = 15 r = 0.05 Present value is calculated as Present Value = ∫ 0 15 2000 e − 0.05 t d t = 2000 ∫ 0 15 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 = 15 , t = − 0.75 Present Value = 2000 ∫ 0 − 0

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Chapter 6.5, Problem 3P

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Find the present and future value of an income stream of $2000 a year for 15 years. The interest rate is 5% compounded continuously.

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Chapter 6.5, Problem 2P

Chapter 6.5, Problem 4P

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Find the present and future value of an income stream of $ 2000 a year for 15 years. The interest rate is 5 % compounded continuously.

Solution Summary: The author calculates the present and future value of an income stream of 2000 a year for 15 years.

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Find the present and future value of an income stream of $2000 a year for 15 years. The interest rate is 5% compounded continuously.

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Chapter 6 Solutions