Explanation Given: There is an income stream of $ 5000 a year for 8 years and the interest rate is 2 % 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 $ 5000 a year for 8 years and the interest rate is 2 % compounded continuously. We have S ( t ) = 5000 M = 8 r = 0.02 Present value is calculated as Present Value = ∫ 0 8 5000 e − 0.02 t d t = 5000 ∫ 0 8 e − 0.02 t d t Solve the integral using fundamental theorem of calculus and substitution method. Let − 0.02 t = u , − 0.02 d t = d u d t = d u − 0.02 Also, when t = 0 , u = 0 When t = 8 , t = − 0.16 Present Value = 5000 ∫ 0 − 0 To determine (b) Explain what present and future values means in terms of income stream.

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 6.5, Problem 4P

To determine

(a)

Find the present and future value of an income stream of $5000 a year for 8 years. The interest rate is 2% compounded continuously.

To determine

(b)

Explain what present and future values means in terms of income stream.

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Chapter 6.5, Problem 3P

Chapter 6.5, Problem 5P

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APPLIED CALCULUS (WILEY PLUS)

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(a) Find the present and future value of an income stream of $ 5000 a year for 8 years. The interest rate is 2 % compounded continuously.

Solution Summary: The author calculates the present and future value of an income stream of 5000 a year for 8 years.

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(a)

Find the present and future value of an income stream of $5000 a year for 8 years. The interest rate is 2% compounded continuously.

(b)

Explain what present and future values means in terms of income stream.

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Chapter 6 Solutions

(a) Find the present and future value of an income stream of $ 5000 a year for 8 years. The interest rate is 2 % compounded continuously.

Solution Summary: The author calculates the present and future value of an income stream of 5000 a year for 8 years.

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(a) Find the present and future value of an income stream of $5000 a year for 8 years. The interest rate is 2% compounded continuously.

(b) Explain what present and future values means in terms of income stream.

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Chapter 6 Solutions

(a)

Find the present and future value of an income stream of $5000 a year for 8 years. The interest rate is 2% compounded continuously.

(b)

Explain what present and future values means in terms of income stream.