Explanation Given: There is an income stream of $ 5000 a year for 4 years and the interest rate is 3 % and 10 % 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 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 When interest rate is 3 % . r = 0.03 Present value is calculated as Present Value = ∫ 0 4 5000 e − 0.03 t d t = 5000 ∫ 0 4 e − 0.03 t d t Solve the integral using fundamental theorem of calculus and substitution method. Let − 0.03 t = u , − 0.03 d t = d u d t = d u − 0.03 Also, when t = 0 , u = 0 When t = 4 , t = − 0.12 Present Value = 5000 ∫ 0 − 0.12 e u d u − 0.03 = 5000 ∫ 0 − 0.12 − 1 0.03 e u d u = 5000 ∫ − 0.12 0 1 0.03 e u d u = 5000 × 1 0.03 ∫ − 0.12 0 e u d u = 5000 × 1 0.03 × [ e u ] − 0.12 0 = 5000 × 1 0 To determine (b) Find the future of the business which expects an income stream of $ 5000 per year for four years and the annual interest rate compounded continuously is 3 % and 10 % .

6th Edition

ISBN: 9781119275565

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 6.5, Problem 10P

To determine

(a)

To find the present of the business which expects an income stream of $5000 per year for four years and the annual interest rate compounded continuously is 3% and 10%.

To determine

(b)

Find the future of the business which expects an income stream of $5000 per year for four years and the annual interest rate compounded continuously is 3% and 10%.

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Chapter 6.5, Problem 9P

Chapter 6.5, Problem 11P

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(a) To find the present of the business which expects an income stream of $ 5000 per year for four years and the annual interest rate compounded continuously is 3 % and 10 % .

Solution Summary: The author calculates the present value of income with interest rate 18833.34, and with r% compounded continuously for M years, using the fundamental theorem of calculus

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(a)

To find the present of the business which expects an income stream of $5000 per year for four years and the annual interest rate compounded continuously is 3% and 10%.

(b)

Find the future of the business which expects an income stream of $5000 per year for four years and the annual interest rate compounded continuously is 3% and 10%.

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Chapter 6 Solutions

(a) To find the present of the business which expects an income stream of $ 5000 per year for four years and the annual interest rate compounded continuously is 3 % and 10 % .

Solution Summary: The author calculates the present value of income with interest rate 18833.34, and with r% compounded continuously for M years, using the fundamental theorem of calculus

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(a) To find the present of the business which expects an income stream of $5000 per year for four years and the annual interest rate compounded continuously is 3% and 10%.

(b) Find the future of the business which expects an income stream of $5000 per year for four years and the annual interest rate compounded continuously is 3% and 10%.

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Chapter 6 Solutions

(a)

To find the present of the business which expects an income stream of $5000 per year for four years and the annual interest rate compounded continuously is 3% and 10%.

(b)

Find the future of the business which expects an income stream of $5000 per year for four years and the annual interest rate compounded continuously is 3% and 10%.