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

To find the present value of the presses, we need to integrate the rate of flow function with respect to time and then discount it to present value using the continuous compounding formula. The integration yields:

∫ 11ea984b_b133_eaba_9029_9fdc385cfdb2_TB4005_11 dt = 11 * e^(-0.07t)

The present value of the presses over 10 years is then:

PV = ∫ 11ea984b_b133_eaba_9029_9fdc385cfdb2_TB4005_11 e^(-0.07t) dt = (11/0.07) * (1 - e^(-0.07*10)) ≈ $181,071

To find the future value of the presses, we can use the continuous compounding formula directly:

FV = PV * e^(0.07*10) ≈ $364,632

Therefore, the best choice is B: Present Value: $181,071; Future Value: $364,632.

Suppose That a Printing Firm Considers the Production of Its