Suppose that a printing firm considers the production of its presses as a continuous income stream. If the annual rate of flow at time t is given by in thousands of dollars per year, and if money is worth 7% compounded continuously, find the present value and future value of the presses over the next 10 years. Round your answer to the nearest dollar.
A) Present Value: $212,562; Future Value: $428,047
B) Present Value: $181,071; Future Value: $364,632
C) Present Value: $119,242; Future Value: $240,124
D) Present Value: $193,878; Future Value: $390,422
E) Present Value: $127,833; Future Value: $257,424

Question

Suppose that a printing firm considers the production of its presses as a continuous income stream. If the annual rate of flow at time t is given by  in thousands of dollars per year, and if money is worth 7% compounded continuously, find the present value and future value of the presses over the next 10 years. Round your answer to the nearest dollar. ​
A) Present Value: $212,562; Future Value: $428,047 
B) Present Value: $181,071; Future Value: $364,632 
C) Present Value: $119,242; Future Value: $240,124 
D) Present Value: $193,878; Future Value: $390,422 
E) Present Value: $127,833; Future Value: $257,424

Quizplus · Accepted Answer

Using the continuous compounding formula, we can calculate the present value and future value of the presses:

PV = ∫0^10 e^(-0.07t) 11e^(0.984t) dt = (11/0.904) [e^(0.984t - 0.07t)]_0^10 = 12.163e^7.168 – 11 = $181,071
FV = ∫0^10 e^(0.07t) 11e^(0.984t) dt = (11/1.054) [e^(0.984t + 0.07t)]_0^10 = 12.163e^8.252 – 11 = $364,632

Rounding to the nearest dollar gives us the answer choice B as the best option.

Suppose That a Printing Firm Considers the Production of Its