Suppose that the profit from a machine's production can be considered as a continuous income stream with annual rate of flow at time t given by (dollars per year). If money is worth 14%, compounded continuously, find the present value of this stream over the next 5 years. Round your answer to the nearest dollar.
A) $26,730
B) $52,226
C) $35,579
D) $28,485
E) $39,326

Question

Suppose that the profit from a machine's production can be considered as a continuous income stream with annual rate of flow at time t given by  (dollars per year). If money is worth 14%, compounded continuously, find the present value of this stream over the next 5 years. Round your answer to the nearest dollar. ​
A) $26,730 
B) $52,226 
C) $35,579 
D) $28,485 
E) $39,326

Quizplus · Accepted Answer

The present value of the continuous income stream from time 0 to time 5 can be calculated using the continuous compounding formula:

PV = ∫0^5 11e^(0.14t) dt = 11/0.14 (e^(0.14t))|0^5 = 78.57(e^(0.7)-1) ≈ $35,579

Therefore, the best choice is C.

Suppose That the Profit from a Machine's Production Can Be