1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ivanshal [37]
3 years ago
8

Suppose that a company needs new equipment, and that the machinery in question earns the company revenue at a continuous rate of

66000t 38000 dollars per year during the first six months of operation, and at the continuous rate of $71000 per year after the first six months. The cost of the machine is $160000. The interest rate is 5% per year, compounded continuously. a) Find the present value of the revenue earned by the machine during the first year of operation. Round your answer to the nearest cent. Value: $ equation editorEquation Editor b) Determine how long it will take for the machine to pay for itself; that is, how long until the present value of the revenue is equal to the cost of the machine. Round your answer to the nearest hundredth. Years: equation editorEquation Editor
Business
1 answer:
julia-pushkina [17]3 years ago
6 0

Answer:

a-The present value of revenue in the first year is $61,085.92.

b-The total time it would take to pay for its price is 2.44 years of 29.33 months.

Explanation:

a-

Let the function of the revenue earned is given as

S(t)=\left \{ {{66000t+38000} {\ \ 0The present value is given as [tex]PV=\int\limits^a_b {S(t)e^{-rt}} \, dt

Here

  • a and b are the limits of integral which are 0 and 1 respectively
  • r is the rate of interest which is 5% or 0.05
  • S(t) is the function of value which is S(t)=\left \{ {{66000t+38000} {\ \ 0So the equation becomes[tex]PV=\int\limits^0_1 {S(t)e^{-0.05t}} \, dt\\PV=\int\limits^{0.5}_0 {(66000t+38000)e^{-0.05t}} \, dt+\int\limits^{1}_{0.5}{(71000)e^{-0.05t}} \, dt\\PV=\int\limits^{0.5}_0 {(66000t)e^{-0.05t}} \, dt+\int\limits^{0.5}_0 {(38000)e^{-0.05t}} \, dt+\int\limits^{1}_{0.5}{(71000)e^{-0.05t}} \, dt\\PV=8113.7805+18764.4669+34207.6751\\PV=61085.9225

    So the present value of revenue in the first year is $61,085.92.

    b-

    The time in which the machine pays for itself is given as

    PV=\int\limits^0_1 {S(t)e^{-0.05t}} \, dt+\int\limits^t_1 {S(t)e^{-0.05t}} \, dt\\PV=61085.9225+\int\limits^{t}_{1}{(71000)e^{-0.05t}} \, dt

    The present value is set equal to the value of machine which is given as

    $160,000 so the equation becomes:

    PV=61085.9225+\int\limits^{t}_{0}{(71000)e^{-0.05t}} \, dt\\160000=61085.9225+\int\limits^{t}_{0}{(71000)e^{-0.05t}} \, dt\\\int\limits^{t}_{0}{(71000)e^{-0.05t}} \, dt=160000-61085.9225\\\int\limits^{t}_{1}{(71000)e^{-0.05t}} \, dt=98914.07\\\\t=-\dfrac{\ln \left(0.93034\right)}{0.05}\\t=1.44496

    So the total time it would take to pay for its price is 2.44 years of 29.33 months.

You might be interested in
(01.02 mc) which of these actions was an economic cause of increased tensions between the north and south?
Damm [24]

The correct option is (b) Protective tariffs

Protective tariffs aim to make imported goods more expensive while protecting domestic producers from overseas rivalry.

<h3 /><h3>What is protective tarrifs?</h3>
  • An illustration of a protective tariff would be the US raising the customs charge on clothing imported from Britain so that it is significantly more expensive than clothing made domestically.
  • The importing countries profit the most from tariffs since they design the policy and receive the cash.
  • The main advantage of tariffs is that they generate income from imported products and services. Tariffs may also serve as a springboard for negotiations between two countries.
  • Protective tariffs are designed to shield vital American industries from international competition, stop foreign manufacturers from dumping inexpensive goods in the US, or both.

Learn more about the Tarrifs with the help of the given link:

brainly.com/question/11672570

#SPJ4

I understand that the question you are looking for is "Which of these actions was an economic cause of increased tensions between the North and South?

(a) Dred Scott decision

(b) Protective tariffs

(c) Bleeding Kansas

(d) Lincoln’s election"

6 0
1 year ago
Jessica does not believe that the methods and processes for determining salary increases in her company are fair. As per this ex
krok68 [10]

Answer:

Procedural justice

Explanation:

Procedural justice is centered on the idea that there should be fairness in the process used in making decision or resolving disputes in a transparent way without being impartial, to ensure the process brings out the right outcomes.

Jessica believes that there’s a problem with the firm’s procedural justice as she believes her firm’s process and methods in determining increase in her salary is not fair enough.

8 0
3 years ago
Heather is sixteen but looks much older. she goes into a jewelry store and buys a diamond bracelet with the money she has been s
brilliants [131]
D is the right answer I suppose
6 0
3 years ago
The Chicago Tribune's published article about BP led to Select one: a. an increase in BP's stock price b. protests c. the positi
never [62]

Answer:

B) Protests

Explanation:

5 0
3 years ago
In the month of April, a department had 600 units in the beginning work in process inventory that were 60% complete. These units
Eduardwww [97]

Answer:

cost to WIP at April 30th: 300,000

        materials  240,000

       conversion  60,000

Explanation:

<em><u>Materials equivalent units:</u></em>

Materials are addedirely at the beginning of the process thus, all are at 100%

transferred out - beginning x percentage of completion + ending x % completion

20,000 - 600 x 100% + 2,000 x 100% =

20,000 - 600 + 2,000 = 21,400

equivalent cost per unit: 2,568,000 / 21,400 = 120

Ending WIP: 2,000 units x 100% x 120 = $ 240,000

<u><em>Conversion equivalent units</em></u>

transferred out - beginning x percentage of completion + ending x % completion

20,000 - 600 x 60% + 2,000 x 20%

20,000 - 360 + 400 = 20,040 units

equivalent cost per unit CC: 3,006,000 / 20,040 = $ 150

Ending WIP_ 2,000 units x 20% x $ 150 = $  60,000

Ending WIP: 240,000 + 60,000 = 300,000 accumulated cost.

7 0
3 years ago
Other questions:
  • ___ is the process of examining, documenting, and assessing the security posture of an organization’s information technology and
    6·1 answer
  • An agent sells his client 10 U.S. government bonds due to mature in 30 years. According to NASAA's Statement of Policy on Unethi
    8·1 answer
  • The Route 66 Gift Shop, which records sales and sales tax separately, had sales on account of $1,500 and cash sales of $1,000. T
    14·1 answer
  • The journal entry to record a return of merchandise purchased on account under a periodic inventory system would be
    6·1 answer
  • How do u maintain your allowance
    10·1 answer
  • Indirect materials and indirect labor are​ ________ for a manufactured product. A. overhead and product costs B. operating and p
    14·1 answer
  • A. What is the significance of voting rights to the ordinary shareholders? What is a proxy? Why do proxy fights occur?
    13·1 answer
  • Insurance Reading Quiz
    11·1 answer
  • The unadjusted trial balance at year-end for a company that uses the percent of receivables method to determine its bad debts ex
    12·1 answer
  • Describe 'the market place' ​
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!