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, we need to use the formula PV = ∫ e^(-0.07t)f(t)dt, where f(t) is the rate of flow at time t. Integrating 11e^(0.05t) from 0 to 10, we get a present value of approximately $181,071.

To find the future value, we can use the formula FV = PV*e^(rt), where r is the continuous interest rate and t is the time period. Plugging in PV = $181,071, r = 0.07, and t = 10, we get a future value of approximately $364,632. Therefore, the best choice is B.

Suppose That a Printing Firm Considers the Production of Its