# 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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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 ### Relevant Questions asked 2021-05-17 You want to invest money for your child's education in a certificate of deposit (CD). You want it to be worth $$12,000$$ in 10 years. How much should you invest if the CD pays interest at a $$9\%$$ annual rate compounded a) Annually? b) Continuously? asked 2021-06-08 How long does it take for an investment to double in value if it is invested at $$14\%$$ compounded quarterly and compounded continuously? a) At $$14\%$$ compounded quarterly, the investment doubles in how many years? b) At $$14\%$$ compounded continuously, the investment doubles in how many years? asked 2021-04-20 (1 pt) A new software company wants to start selling DVDs withtheir product. The manager notices that when the price for a DVD is19 dollars, the company sells 140 units per week. When the price is28 dollars, the number of DVDs sold decreases to 90 units per week.Answer the following questions: A. Assume that the demand curve is linear. Find the demand, q, as afunction of price, p. Answer: q= B. Write the revenue function, as a function of price. Answer:R(p)= C. Find the price that maximizes revenue. Hint: you may sketch thegraph of the revenue function. Round your answer to the closestdollar. Answer: D. Find the maximum revenue. Answer: asked 2021-05-08 Write an exponential growth or decay function to model each situation. Then find the value of the function after the given amount of time. A new car is worth$25,000, and its value decreases by 15% each year; 6 years.
4.7 A multiprocessor with eight processors has 20attached tape drives. There is a large number of jobs submitted tothe system that each require a maximum of four tape drives tocomplete execution. Assume that each job starts running with onlythree tape drives for a long period before requiring the fourthtape drive for a short period toward the end of its operation. Alsoassume an endless supply of such jobs.
a) Assume the scheduler in the OS will not start a job unlessthere are four tape drives available. When a job is started, fourdrives are assigned immediately and are not released until the jobfinishes. What is the maximum number of jobs that can be inprogress at once? What is the maximum and minimum number of tapedrives that may be left idle as a result of this policy?
b) Suggest an alternative policy to improve tape driveutilization and at the same time avoid system deadlock. What is themaximum number of jobs that can be in progress at once? What arethe bounds on the number of idling tape drives?
The value of good wine increases with age. Thus, if you are a wine dealer, you have the problem of deciding whether to sell your wine now, at a price of $P a bottle, or to sell it later at a higher price. Suppose you know that the amount a wine-drinker is willing to pay for a bottle of this wine t years from now is$P(1+20?t). Assuming continuous compounding and a prevailing interest rate of 5% per year, when is the best time to sell your wine?
Finance bonds/dividends/loans exercises, need help or formulas
Some of the exercises, calculating the Ri is clear, but then i got stuck:
A security pays a yearly dividend of 7€ during 5 years, and on the 5th year we could sell it at a price of 75€, market rate is 19%, risk free rate 2%, beta 1,8. What would be its price today? 2.1 And if its dividend growths 1,7% each year along these 5 years-what would be its price?
A security pays a constant dividend of 0,90€ during 5 years and thereafter will be sold at 10 €, market rate 18%, risk free rate 2,5%, beta 1,55, what would be its price today?
At what price have i purchased a security if i already made a 5€ profit, and this security pays dividends as follows: first year 1,50 €, second year 2,25€, third year 3,10€ and on the 3d year i will sell it for 18€. Market rate is 8%, risk free rate 0,90%, beta=2,3.
What is the original maturity (in months) for a ZCB, face value 2500€, required rate of return 16% EAR if we paid 700€ and we bought it 6 month after the issuance, and actually we made an instant profit of 58,97€
You'll need 10 Vespas for your Parcel Delivery Business. Each Vespa has a price of 2850€ fully equipped. Your bank is going to fund this operation with a 5 year loan, 12% nominal rate at the beginning, and after increasing 1% every year. You'll have 5 years to fully amortize this loan. You want tot make monthly installments. At what price should you sell it after 3 1/2 years to lose only 10% of the remaining debt.
An airplane propeller is 2.08 m in length (from tip to tip) and has a mass of 117 kg. When the airpline's engine is first started, it applies a constant torque of $$\displaystyle{1950}\ {N}\cdot{m}$$ to the propeller, which starts from rest.
a) What is the angular acceleration of the propeller? Model the propeller as a slender rod.
b) What is the propeller's angular speed after making 5.00 revolutions?
c) How much work is done by the engine during the first 5.00 revolutions?
e) What is the instantaneous power output of the motor at the instant that the propeller has turne through 5.00 revolutions?
Bethany needs to borrow $$10,000.$$ She can borrow the money at $$5.5\%$$ simple interest for 4 yr or she can borrow at $$5\%$$ with interest compounded continuously for 4 yr.
a) How much total interest would Bethany pay at $$5.5\%$$ simple interest?
b) How much total interest would Bethany pay at $$5%$$ interest compounded continuously?
You deposit money into a saving account that earns interest. The balance Bo f the account after t years is given by $$\displaystyle{B}={1200}\cdot{1.05}^{{t}}{d}{o}{l}{l}{a}{r}{s}.$$