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

We can use the formula for continuous compounding to find the present and future values:

Present Value = ∫e^(-0.07t) * 11000e^(0.1t) dt from t = 0 to t = 10
Present Value = 11000/0.17 (e^0.03 - e^(-0.07*10))
Present Value ≈ $181,071

Future Value = 11000/0.07 (e^(0.07*10) - 1) - Present Value
Future Value ≈ $364,632

Therefore, the best choice is B.

Suppose That a Printing Firm Considers the Production of Its