A recently installed machine earns the company revenue at a continuous rate of 5
ID: 3284554 • Letter: A
Question
A recently installed machine earns the company revenue at a continuous rate of 50,000e^.11334 dollars per year during the first year of operation and at the constant continuous rate of 56,000 dollars per year after the first year. The cost of the machine is $400,000, the interest rate is 5% per year, compounded continuously, and t is in years since the machine was installed. Determine 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. Give your result as a number of years, accurate to two decimal places.Explanation / Answer
revenue for first year = 50000*e^0.1134 lets say it takes t more year to payback , therefore revenue earned in t years is =56000*t total revenue = 50000*e^0.1134+ 56000*t therefore total years = t+1 cost of machine after t+1 yrs = initial cost + compound interest = 400000*e^(0.05*(t+1)) total revenue = total cost of machine , gives 50000*e^0.1134 + 56000*t=400000*e^(0.05*(t+1)) solving above we get t= 14.52 yrs Therefore total years = t+1 = 15.52 yrs (answer)