Explanation Given information: The new machine costs $130,000 and earns profit at the continuous rate of $80,000 per year. The interest rate is 8.5% per year compounded continuously. Formula used: Present value , P = ∫ 0 M S ( t ) e − r t d t Where S ( t ) is sale rate per year, t is the time, P is present value and r is rate of interest. Calculation: The present value of the revenue generated by the machine in M years is: P = ∫ 0 M 80 , 000 ⋅ e − 0.085 t d t = 80 , 000 ( e − 0.085 t − 0.085 ) 0 M = 80 , 000 − 0

6th Edition

ISBN: 9781119267874

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 6.5, Problem 22P

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The time taken for the machine to pay for itself.

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Chapter 6.5, Problem 21P

Chapter 6.5, Problem 23P

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The time taken for the machine to pay for itself.

Solution Summary: The author calculates the time taken for the machine to pay for itself. The new machine costs 130,000 and earns profit at the continuous rate of 80,000 per year.

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To find: The time taken for the machine to pay for itself.

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Chapter 6 Solutions

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The time taken for the machine to pay for itself.