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

We can use the formula for continuous compounding:

PV = ∫0^5 [11e^(0.14t)]e^(-0.14t) dt = 11 ∫0^5 e^(0.14t - 0.14t) dt
PV = 11 ∫0^5 e^(0.14t) dt = 11/0.14 [e^(0.14t)]_0^5 = 11/0.14 [e^(0.7) - 1]
PV ≈ $35,579 (rounded to the nearest dollar)

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