(a) Explanation Given Information: Provided information is: Profit is P = $ 75 , 000 and annually interest rate is r = 8 % . Formula used: Present value of Perpetuity: Present value = P ∫ 0 t e − r t d t Here, P is the size of each annual payment, t is the time and r is the annual interest rate in decimal form. Calculation: Consider the provided information and recall the formula for present value. Present value = P ∫ 0 t e − r t d t Interest in fraction form is: r = 8 % = 8 100 = 0.08 Substitute $ 75 , 000 for P and 0 (b) To determine The present value of the farm if the continuous flow of profit at rate of $ 75 , 000 per year and interest rate is 8 % compounded continuously for forever.

Calculus: An Applied Approach (MindTap Course List)

10th Edition

ISBN: 9781305860919

Author: Ron Larson

Publisher: Cengage Learning

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Question

Chapter 6.4, Problem 38E

(a)

To determine

To calculate: The present value of the farm if the continuous flow of profit at rate of $75,000 per year and interest rate is 8% compounded continuously for 20 years.

(b)

To determine

The present value of the farm if the continuous flow of profit at rate of $75,000 per year and interest rate is 8% compounded continuously for forever.

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Chapter 6.4, Problem 37E

Chapter 6.4, Problem 39E

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Chapter 6 Solutions

Calculus: An Applied Approach (MindTap Course List)

Ch. 6.1 - Prob. 1CP Ch. 6.1 - Prob. 2CP Ch. 6.1 - Prob. 3CP Ch. 6.1 - Prob. 4CP Ch. 6.1 - Prob. 5CP Ch. 6.1 - Prob. 6CP Ch. 6.1 - Prob. 7CP Ch. 6.1 - Prob. 1SWU Ch. 6.1 - Prob. 2SWU Ch. 6.1 - Prob. 3SWU

Ch. 6.1 - Prob. 4SWU Ch. 6.1 - Prob. 5SWU Ch. 6.1 - Prob. 6SWU Ch. 6.1 - Prob. 7SWU Ch. 6.1 - Prob. 8SWU Ch. 6.1 - Prob. 9SWU Ch. 6.1 - Prob. 10SWU Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Integration by Parts In Exercises 5-16, use...Ch. 6.1 - Prob. 6E Ch. 6.1 - Integration by Parts In Exercises 5-16, use...Ch. 6.1 - Prob. 8E Ch. 6.1 - Integration by Parts In Exercises 5-16, use...Ch. 6.1 - Prob. 10E Ch. 6.1 - Integration by Parts In Exercises 5-16, use...Ch. 6.1 - Prob. 12E Ch. 6.1 - Integration by Parts In Exercises 5-16, use...Ch. 6.1 - Prob. 14E Ch. 6.1 - Integration by Parts In Exercises 5-16, use...Ch. 6.1 - Prob. 16E Ch. 6.1 - Prob. 17E Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Finding an Indefinite Integral In Exercises 17-38,...Ch. 6.1 - Finding an Indefinite Integral In Exercises 17-38,...Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Finding an Indefinite Integral In Exercises 17-38,...Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Prob. 31E Ch. 6.1 - Prob. 32E Ch. 6.1 - Prob. 33E Ch. 6.1 - Prob. 34E Ch. 6.1 - Prob. 35E Ch. 6.1 - Prob. 36E Ch. 6.1 - Finding an Indefinite Integral In Exercises 17-38,...Ch. 6.1 - Finding an Indefinite Integral In Exercises 17-38,...Ch. 6.1 - Prob. 39E Ch. 6.1 - Prob. 40E Ch. 6.1 - Prob. 41E Ch. 6.1 - Evaluating a Definite Integral In Exercises 39-46,...Ch. 6.1 - Prob. 43E Ch. 6.1 - Prob. 44E Ch. 6.1 - Prob. 45E Ch. 6.1 - Prob. 46E Ch. 6.1 - Prob. 47E Ch. 6.1 - Prob. 48E Ch. 6.1 - Prob. 49E Ch. 6.1 - Prob. 50E Ch. 6.1 - Prob. 51E Ch. 6.1 - Prob. 52E Ch. 6.1 - Verifying Formulas In Exercises 53 and 54, use...Ch. 6.1 - Verifying Formulas In Exercises 53 and 54, use...Ch. 6.1 - Prob. 55E Ch. 6.1 - Prob. 56E Ch. 6.1 - Prob. 57E Ch. 6.1 - Prob. 58E Ch. 6.1 - Prob. 59E Ch. 6.1 - Prob. 60E Ch. 6.1 - Prob. 61E Ch. 6.1 - Prob. 62E Ch. 6.1 - Prob. 63E Ch. 6.1 - Prob. 64E Ch. 6.1 - Prob. 65E Ch. 6.1 - Revenue A company sells a seasonal product. The...Ch. 6.1 - Prob. 67E Ch. 6.1 - Prob. 68E Ch. 6.1 - Prob. 69E Ch. 6.1 - Prob. 70E Ch. 6.1 - Prob. 71E Ch. 6.1 - Prob. 72E Ch. 6.1 - Prob. 73E Ch. 6.1 - Prob. 74E Ch. 6.1 - Prob. 75E Ch. 6.1 - Prob. 76E Ch. 6.1 - Prob. 77E Ch. 6.1 - Prob. 78E Ch. 6.1 - Prob. 79E Ch. 6.1 - Future Value In Exercises 79 and 80, find the...Ch. 6.1 - Prob. 81E Ch. 6.1 - Prob. 82E Ch. 6.2 - Checkpoint 1 Use the integration table in Appendix...Ch. 6.2 - Prob. 2CP Ch. 6.2 - Prob. 3CP Ch. 6.2 - Prob. 4CP Ch. 6.2 - Checkpoint 5 Use the integration table in Appendix...Ch. 6.2 - Prob. 6CP Ch. 6.2 - Prob. 1SWU Ch. 6.2 - Prob. 2SWU Ch. 6.2 - Prob. 3SWU Ch. 6.2 - Prob. 4SWU Ch. 6.2 - Prob. 5SWU Ch. 6.2 - Prob. 6SWU Ch. 6.2 - Prob. 1E Ch. 6.2 - Prob. 2E Ch. 6.2 - Using Integration Tables In Exercises 18, use the...Ch. 6.2 - Prob. 4E Ch. 6.2 - Prob. 5E Ch. 6.2 - Prob. 6E Ch. 6.2 - Prob. 7E Ch. 6.2 - Prob. 8E Ch. 6.2 - Prob. 9E Ch. 6.2 - Prob. 10E Ch. 6.2 - Prob. 11E Ch. 6.2 - Prob. 12E Ch. 6.2 - Prob. 13E Ch. 6.2 - 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Prob. 58E Ch. 6.2 - Prob. 59E Ch. 6.2 - Prob. 60E Ch. 6.2 - Prob. 61E Ch. 6.2 - Prob. 1QY Ch. 6.2 - Prob. 2QY Ch. 6.2 - Prob. 3QY Ch. 6.2 - In Exercises 16, use integration by parts to find...Ch. 6.2 - Prob. 5QY Ch. 6.2 - Prob. 6QY Ch. 6.2 - Prob. 7QY Ch. 6.2 - Prob. 8QY Ch. 6.2 - Prob. 9QY Ch. 6.2 - Prob. 10QY Ch. 6.2 - Prob. 11QY Ch. 6.2 - Prob. 12QY Ch. 6.2 - Prob. 13QY Ch. 6.2 - Prob. 14QY Ch. 6.2 - Prob. 15QY Ch. 6.2 - Prob. 16QY Ch. 6.2 - Prob. 17QY Ch. 6.2 - Prob. 18QY Ch. 6.2 - Prob. 19QY Ch. 6.2 - Prob. 20QY Ch. 6.2 - Prob. 21QY Ch. 6.3 - Checkpoint 1 Use the Trapezoidal Rule with n = 4...Ch. 6.3 - Prob. 2CP Ch. 6.3 - Prob. 3CP Ch. 6.3 - Prob. 1SWU Ch. 6.3 - Prob. 2SWU Ch. 6.3 - Prob. 3SWU Ch. 6.3 - Prob. 4SWU Ch. 6.3 - Prob. 5SWU Ch. 6.3 - Prob. 6SWU Ch. 6.3 - Prob. 7SWU Ch. 6.3 - Prob. 8SWU Ch. 6.3 - Prob. 9SWU Ch. 6.3 - Prob. 10SWU Ch. 6.3 - Prob. 1E Ch. 6.3 - Prob. 2E Ch. 6.3 - Prob. 3E Ch. 6.3 - Prob. 4E Ch. 6.3 - Prob. 5E Ch. 6.3 - Prob. 6E Ch. 6.3 - Prob. 7E Ch. 6.3 - Prob. 8E Ch. 6.3 - Prob. 9E Ch. 6.3 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6.3 - Prob. 11E Ch. 6.3 - Prob. 12E Ch. 6.3 - Prob. 13E Ch. 6.3 - Prob. 14E Ch. 6.3 - Prob. 15E Ch. 6.3 - Prob. 16E Ch. 6.3 - Prob. 17E Ch. 6.3 - Prob. 18E Ch. 6.3 - Prob. 19E Ch. 6.3 - Prob. 20E Ch. 6.3 - Prob. 31E Ch. 6.3 - Prob. 32E Ch. 6.3 - Prob. 33E Ch. 6.3 - Prob. 34E Ch. 6.3 - Prob. 35E Ch. 6.3 - Prob. 36E Ch. 6.3 - Prob. 37E Ch. 6.3 - Prob. 38E Ch. 6.3 - Prob. 39E Ch. 6.3 - Error Analysis In Exercises 37-40, use the error...Ch. 6.3 - Prob. 43E Ch. 6.3 - Electricity The table shows the residential prices...Ch. 6.3 - Prob. 45E Ch. 6.3 - Prob. 46E Ch. 6.3 - Prob. 47E Ch. 6.3 - Prob. 48E Ch. 6.4 - Prob. 1CP Ch. 6.4 - Prob. 2CP Ch. 6.4 - Prob. 3CP Ch. 6.4 - Prob. 4CP Ch. 6.4 - Prob. 5CP Ch. 6.4 - Prob. 1SWU Ch. 6.4 - Prob. 2SWU Ch. 6.4 - Prob. 3SWU Ch. 6.4 - Prob. 4SWU Ch. 6.4 - Prob. 5SWU Ch. 6.4 - Prob. 6SWU Ch. 6.4 - Prob. 7SWU Ch. 6.4 - Prob. 8SWU Ch. 6.4 - Prob. 9SWU Ch. 6.4 - Prob. 10SWU Ch. 6.4 - Prob. 1E Ch. 6.4 - 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Prob. 8RE Ch. 6 - Prob. 9RE Ch. 6 - Prob. 10RE Ch. 6 - Prob. 11RE Ch. 6 - Prob. 12RE Ch. 6 - Prob. 13RE Ch. 6 - Prob. 14RE Ch. 6 - Finding Present Value In Exercises 1316, find the...Ch. 6 - Prob. 16RE Ch. 6 - Prob. 17RE Ch. 6 - Prob. 18RE Ch. 6 - Prob. 19RE Ch. 6 - Prob. 20RE Ch. 6 - Prob. 21RE Ch. 6 - Prob. 22RE Ch. 6 - Prob. 23RE Ch. 6 - Prob. 24RE Ch. 6 - Prob. 25RE Ch. 6 - Prob. 26RE Ch. 6 - Prob. 27RE Ch. 6 - Prob. 28RE Ch. 6 - Prob. 29RE Ch. 6 - Prob. 30RE Ch. 6 - Prob. 31RE Ch. 6 - Prob. 32RE Ch. 6 - Prob. 33RE Ch. 6 - Prob. 34RE Ch. 6 - Prob. 35RE Ch. 6 - Prob. 36RE Ch. 6 - Prob. 37RE Ch. 6 - Prob. 38RE Ch. 6 - Prob. 39RE Ch. 6 - Prob. 40RE Ch. 6 - Prob. 41RE Ch. 6 - Prob. 42RE Ch. 6 - Prob. 43RE Ch. 6 - Prob. 44RE Ch. 6 - Prob. 45RE Ch. 6 - Prob. 46RE Ch. 6 - Prob. 47RE Ch. 6 - Prob. 48RE Ch. 6 - Prob. 49RE Ch. 6 - Prob. 50RE Ch. 6 - Prob. 51RE Ch. 6 - Prob. 52RE Ch. 6 - Prob. 53RE Ch. 6 - Prob. 54RE Ch. 6 - Prob. 55RE Ch. 6 - Prob. 56RE Ch. 6 - Prob. 57RE Ch. 6 - Prob. 58RE Ch. 6 - Prob. 59RE Ch. 6 - Prob. 60RE Ch. 6 - Endowment In Exercises 61 and 62, determine the...Ch. 6 - Prob. 62RE Ch. 6 - Prob. 63RE Ch. 6 - Prob. 64RE Ch. 6 - Prob. 1TYS Ch. 6 - Prob. 2TYS Ch. 6 - Prob. 3TYS Ch. 6 - Prob. 4TYS Ch. 6 - Prob. 5TYS Ch. 6 - Prob. 6TYS Ch. 6 - Prob. 7TYS Ch. 6 - Prob. 8TYS Ch. 6 - Prob. 9TYS Ch. 6 - Prob. 10TYS Ch. 6 - Prob. 11TYS Ch. 6 - Prob. 12TYS Ch. 6 - Prob. 13TYS Ch. 6 - Prob. 14TYS Ch. 6 - Prob. 15TYS Ch. 6 - Prob. 16TYS Ch. 6 - Prob. 17TYS Ch. 6 - Prob. 18TYS

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The present value of the farm if the continuous flow of profit at rate of $ 75 , 000 per year and interest rate is 8 % compounded continuously for 20 years .

Solution Summary: The author calculates the present value of the farm if the continuous flow of profit at rate of 75,000 per year and interest rate is 8%