A recently-installed machine earns the company revenueat a continuous rate of 60,000t + 45,000 dollars per year duringthe first six months of operation and at the continuous rate of75,000 dollars per year after the first six months. The cost of themachine is $150,000, the interest rate is 7% per year, compoundedcontinuously, and t is time in years since the machine wasinstalled. (a)Find the present value of the revenue earned by the machineduring the first year of operation. (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 revenueto equal the cost of the machine?

A recently-installed machine earns the company revenueat a continuous rate of 60,000t + 45,000 dollars per year duringthe first six months of operation and at the continuous rate of75,000 dollars per year after the first six months. The cost of themachine is $150,000, the interest rate is 7% per year, compoundedcontinuously, and t is time in years since the machine wasinstalled. (a)Find the present value of the revenue earned by the machineduring the first year of operation. (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 revenueto equal the cost of the machine?

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asked 2021-01-24
A recently-installed machine earns the company revenueat a continuous rate of 60,000t + 45,000 dollars per year duringthe first six months of operation and at the continuous rate of75,000 dollars per year after the first six months. The cost of themachine is $150,000, the interest rate is 7% per year, compoundedcontinuously, and t is time in years since the machine wasinstalled.
(a)Find the present value of the revenue earned by the machineduring the first year of operation.
(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 revenueto equal the cost of the machine?

Answers (1)

2021-01-25
i am trying to provide a hint i think this will be useful for you (a) present value = \(\displaystyle{\int_{{{0}}}^{{{1}}}}{\left({60000}{t}+{45000}\right)}{e}^{{{0.07}{t}}}{\left.{d}{t}\right.}\)
(b) present value. e0.07 M = 150000 solve this for finding the time M please verify the answer , i am not sure
0

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