A recently installed machine earns the company revenue at a continuous rate of 60,000t + 45,000 dollars per year during the f six months of operation and at the continuous rate of 75,000 dollars per year after the first six months. The cost of the machine $153,000, the interest rate is 7% per year, compounded continuously, and t is time in years since the machine was installed. (a) Find the present value of the revenue earned by the machine during the first year of operation. Round your answer to the nearest integer. $ 65022 (b) Find how long it will take for the machine to pay for itself; that is, how long it will take for the present value of the revenue to equal the cost of the machine?
A recently installed machine earns the company revenue at a continuous rate of 60,000t + 45,000 dollars per year during the f six months of operation and at the continuous rate of 75,000 dollars per year after the first six months. The cost of the machine $153,000, the interest rate is 7% per year, compounded continuously, and t is time in years since the machine was installed. (a) Find the present value of the revenue earned by the machine during the first year of operation. Round your answer to the nearest integer. $ 65022 (b) Find how long it will take for the machine to pay for itself; that is, how long it will take for the present value of the revenue to equal the cost of the machine?
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Transcribed Image Text:A recently installed machine earns the company revenue at a continuous rate of 60,000t + 45,000 dollars per year during the first
six months of operation and at the continuous rate of 75,000 dollars per year after the first six months. The cost of the machine is
$153,000, the interest rate is 7% per year, compounded continuously, and t is time in years since the machine was installed.
(a) Find the present value of the revenue earned by the machine during the first year of operation.
Round your answer to the nearest integer.
65022
(b) Find how long it will take for the machine to pay for itself; that is, how long it will take for the present value of the revenue to
equal the cost of the machine?
Round your answer to two decimal places.
1.69
years
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