Mathematical Applications for the ...

11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

Suppose that a vending machine company is considering selling some of its machines. Suppose further that the income from these particular machines is a continuous stream with an annual rate of flow at time t given by

f ( t ) = 12 e − 0.4 ( t + 3 ) in thousands of dollars per year. Find the present value and future value of the machines over the next 5 years if money is worth 10 % compounded continuously.

To determine

To calculate: The present value and future value of the vending machine company whose income stream for next 5 years from 10% compounded continuously income stream is approximated by f(t)=12e−0.4(t+3) thousands dollars per year. Whereby, t is the rate of flow at time yearly.

Explanation

Given Information:

The present value and future value of the vending machine company whose income stream for next 5 years from 10% compounded continuously income stream is approximated by f(t)=12e−0.4(t+3) thousands dollars per year. Whereby, t is the rate of flow at time yearly.

Formula used:

According to the present value of a continuous income stream:

If f(t) is the continuous income flow earning interest at rate compounded continuously with t=0 to t=k is the time interval, then the Present Value of a continuous income stream is:

Present value=∫0kf(t)e−rtdt.

And

According to the future value of a continuous income stream:

If f(t) is the rate of continuous income flow for k years earning interest at rate r compounded continuously, then the present value of a continuous income stream is:

Future value=erk∫0kf(t)e−rtdt.

Calculation:

Consider the income equation:

f(t)=12e−0.4(t+3)

Since, the income to be calculated for next 5 years:

Thus

k=5

And

Money is worth 10% compounded continuously,

Thus,

r=0.10

Considering the formula:

Present value=∫0kf(t)e−rtdt

Substituting 5 for k, 0.10 for r and 12e−0.4(t+3) for f(t) to get:

Present value=∫0512e−0.4(t+3).e−0.10tdt=∫0512e−0.5t−1.2dt=−24∫0512e−0.5t−1.2(0.5)dt=[−24e−0.5t−1.2]05

Solving the limit of the function to get:

Present value=[−24e−0.5(5)−1.2]−[−24e−0

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Sect-13.1 P-1CP Sect-13.1 P-2CP Sect-13.1 P-1E Sect-13.1 P-2E Sect-13.1 P-3E Sect-13.1 P-4E Sect-13.1 P-5E Sect-13.1 P-6E Sect-13.1 P-7E Sect-13.1 P-8E

Sect-13.1 P-9E Sect-13.1 P-10E Sect-13.1 P-11E Sect-13.1 P-12E Sect-13.1 P-13E Sect-13.1 P-14E Sect-13.1 P-15E Sect-13.1 P-16E Sect-13.1 P-17E Sect-13.1 P-18E Sect-13.1 P-19E Sect-13.1 P-20E Sect-13.1 P-21E Sect-13.1 P-22E Sect-13.1 P-23E Sect-13.1 P-24E Sect-13.1 P-25E Sect-13.1 P-26E Sect-13.1 P-27E Sect-13.1 P-28E Sect-13.1 P-29E Sect-13.1 P-30E Sect-13.1 P-31E Sect-13.1 P-32E Sect-13.1 P-33E Sect-13.1 P-34E Sect-13.1 P-35E Sect-13.1 P-36E Sect-13.1 P-37E Sect-13.1 P-38E Sect-13.1 P-39E Sect-13.1 P-40E Sect-13.2 P-1CP Sect-13.2 P-2CP Sect-13.2 P-1E Sect-13.2 P-2E Sect-13.2 P-3E Sect-13.2 P-4E Sect-13.2 P-5E Sect-13.2 P-6E Sect-13.2 P-9E Sect-13.2 P-10E Sect-13.2 P-11E Sect-13.2 P-12E Sect-13.2 P-7E Sect-13.2 P-8E Sect-13.2 P-23E Sect-13.2 P-24E Sect-13.2 P-13E Sect-13.2 P-14E Sect-13.2 P-15E Sect-13.2 P-16E Sect-13.2 P-17E Sect-13.2 P-18E Sect-13.2 P-19E Sect-13.2 P-20E Sect-13.2 P-21E Sect-13.2 P-22E Sect-13.2 P-25E Sect-13.2 P-26E Sect-13.2 P-27E Sect-13.2 P-28E Sect-13.2 P-29E Sect-13.2 P-30E Sect-13.2 P-31E Sect-13.2 P-32E Sect-13.2 P-33E Sect-13.2 P-34E Sect-13.2 P-35E Sect-13.2 P-36E Sect-13.2 P-37E Sect-13.2 P-38E Sect-13.2 P-39E Sect-13.2 P-40E Sect-13.2 P-41E Sect-13.2 P-42E Sect-13.2 P-43E Sect-13.2 P-44E Sect-13.2 P-45E Sect-13.2 P-46E Sect-13.2 P-47E Sect-13.2 P-48E Sect-13.2 P-49E Sect-13.2 P-50E Sect-13.2 P-51E Sect-13.2 P-52E Sect-13.2 P-53E Sect-13.2 P-54E Sect-13.2 P-55E Sect-13.2 P-56E Sect-13.2 P-57E Sect-13.2 P-58E Sect-13.2 P-59E Sect-13.2 P-60E Sect-13.2 P-61E Sect-13.2 P-62E Sect-13.2 P-63E Sect-13.2 P-64E Sect-13.2 P-65E Sect-13.2 P-66E Sect-13.2 P-67E Sect-13.2 P-68E Sect-13.3 P-1CP Sect-13.3 P-2CP Sect-13.3 P-3CP Sect-13.3 P-1E Sect-13.3 P-2E Sect-13.3 P-3E Sect-13.3 P-4E Sect-13.3 P-5E Sect-13.3 P-6E Sect-13.3 P-7E Sect-13.3 P-8E Sect-13.3 P-9E Sect-13.3 P-10E Sect-13.3 P-11E Sect-13.3 P-12E Sect-13.3 P-13E Sect-13.3 P-14E Sect-13.3 P-15E Sect-13.3 P-16E Sect-13.3 P-17E Sect-13.3 P-18E Sect-13.3 P-19E Sect-13.3 P-20E Sect-13.3 P-21E Sect-13.3 P-22E Sect-13.3 P-23E Sect-13.3 P-24E Sect-13.3 P-25E Sect-13.3 P-26E Sect-13.3 P-27E Sect-13.3 P-28E Sect-13.3 P-29E Sect-13.3 P-30E Sect-13.3 P-31E Sect-13.3 P-32E Sect-13.3 P-33E Sect-13.3 P-34E Sect-13.3 P-35E Sect-13.3 P-36E Sect-13.3 P-37E Sect-13.3 P-38E Sect-13.3 P-39E Sect-13.3 P-40E Sect-13.3 P-41E Sect-13.3 P-42E Sect-13.3 P-43E Sect-13.3 P-44E Sect-13.3 P-45E Sect-13.3 P-46E Sect-13.3 P-47E Sect-13.3 P-48E Sect-13.3 P-49E Sect-13.3 P-50E Sect-13.4 P-1CP Sect-13.4 P-2CP Sect-13.4 P-3CP Sect-13.4 P-1E Sect-13.4 P-2E Sect-13.4 P-3E Sect-13.4 P-4E Sect-13.4 P-5E Sect-13.4 P-6E Sect-13.4 P-7E Sect-13.4 P-8E Sect-13.4 P-9E Sect-13.4 P-10E Sect-13.4 P-11E Sect-13.4 P-12E Sect-13.4 P-13E Sect-13.4 P-14E Sect-13.4 P-15E Sect-13.4 P-16E Sect-13.4 P-17E Sect-13.4 P-18E Sect-13.4 P-19E Sect-13.4 P-20E Sect-13.4 P-21E Sect-13.4 P-22E Sect-13.4 P-23E Sect-13.4 P-24E Sect-13.4 P-25E Sect-13.4 P-26E Sect-13.4 P-27E Sect-13.4 P-28E Sect-13.4 P-29E Sect-13.4 P-30E Sect-13.4 P-31E Sect-13.4 P-32E Sect-13.4 P-33E Sect-13.4 P-34E Sect-13.4 P-35E Sect-13.4 P-36E Sect-13.5 P-1CP Sect-13.5 P-2CP Sect-13.5 P-3CP Sect-13.5 P-4CP Sect-13.5 P-5CP Sect-13.5 P-6CP Sect-13.5 P-1E Sect-13.5 P-2E Sect-13.5 P-3E Sect-13.5 P-4E Sect-13.5 P-5E Sect-13.5 P-6E Sect-13.5 P-7E Sect-13.5 P-8E Sect-13.5 P-9E Sect-13.5 P-10E Sect-13.5 P-11E Sect-13.5 P-12E Sect-13.5 P-13E Sect-13.5 P-14E Sect-13.5 P-15E Sect-13.5 P-16E Sect-13.5 P-17E Sect-13.5 P-18E Sect-13.5 P-19E Sect-13.5 P-20E Sect-13.5 P-21E Sect-13.5 P-22E Sect-13.5 P-23E Sect-13.5 P-24E Sect-13.5 P-25E Sect-13.5 P-26E Sect-13.5 P-27E Sect-13.5 P-28E Sect-13.5 P-29E Sect-13.5 P-30E Sect-13.5 P-31E Sect-13.5 P-32E Sect-13.5 P-33E Sect-13.5 P-34E Sect-13.5 P-35E Sect-13.5 P-36E Sect-13.5 P-37E Sect-13.5 P-38E Sect-13.5 P-39E Sect-13.5 P-40E Sect-13.5 P-41E Sect-13.5 P-42E Sect-13.6 P-1CP Sect-13.6 P-2CP Sect-13.6 P-1E Sect-13.6 P-2E Sect-13.6 P-3E Sect-13.6 P-4E Sect-13.6 P-5E Sect-13.6 P-6E Sect-13.6 P-7E Sect-13.6 P-8E Sect-13.6 P-9E Sect-13.6 P-10E Sect-13.6 P-11E Sect-13.6 P-12E Sect-13.6 P-13E Sect-13.6 P-14E Sect-13.6 P-15E Sect-13.6 P-16E Sect-13.6 P-17E Sect-13.6 P-18E Sect-13.6 P-19E Sect-13.6 P-20E Sect-13.6 P-21E Sect-13.6 P-22E Sect-13.6 P-23E Sect-13.6 P-24E Sect-13.6 P-25E Sect-13.6 P-26E Sect-13.6 P-27E Sect-13.6 P-28E Sect-13.6 P-29E Sect-13.6 P-30E Sect-13.6 P-31E Sect-13.6 P-32E Sect-13.6 P-33E Sect-13.6 P-34E Sect-13.6 P-35E Sect-13.6 P-36E Sect-13.6 P-37E Sect-13.6 P-38E Sect-13.7 P-1CP Sect-13.7 P-2CP Sect-13.7 P-1E Sect-13.7 P-2E Sect-13.7 P-3E Sect-13.7 P-4E Sect-13.7 P-5E Sect-13.7 P-6E Sect-13.7 P-7E Sect-13.7 P-8E Sect-13.7 P-9E Sect-13.7 P-10E Sect-13.7 P-11E Sect-13.7 P-12E Sect-13.7 P-13E Sect-13.7 P-14E Sect-13.7 P-15E Sect-13.7 P-16E Sect-13.7 P-17E Sect-13.7 P-18E Sect-13.7 P-19E Sect-13.7 P-20E Sect-13.7 P-21E Sect-13.7 P-22E Sect-13.7 P-23E Sect-13.7 P-24E Sect-13.7 P-25E Sect-13.7 P-26E Sect-13.7 P-27E Sect-13.7 P-28E Sect-13.7 P-29E Sect-13.7 P-30E Sect-13.7 P-31E Sect-13.7 P-32E Sect-13.7 P-33E Sect-13.7 P-34E Sect-13.7 P-35E Sect-13.7 P-36E Sect-13.7 P-37E Sect-13.7 P-38E Sect-13.7 P-39E Sect-13.7 P-40E Sect-13.7 P-41E Sect-13.7 P-42E Sect-13.7 P-43E Sect-13.7 P-44E Sect-13.7 P-45E Sect-13.7 P-47E Sect-13.8 P-1CP Sect-13.8 P-2CP Sect-13.8 P-3CP Sect-13.8 P-1E Sect-13.8 P-2E Sect-13.8 P-3E Sect-13.8 P-4E Sect-13.8 P-5E Sect-13.8 P-6E Sect-13.8 P-7E Sect-13.8 P-8E Sect-13.8 P-9E Sect-13.8 P-10E Sect-13.8 P-11E Sect-13.8 P-12E Sect-13.8 P-13E Sect-13.8 P-14E Sect-13.8 P-15E Sect-13.8 P-16E Sect-13.8 P-17E Sect-13.8 P-18E Sect-13.8 P-19E Sect-13.8 P-20E Sect-13.8 P-21E Sect-13.8 P-22E Sect-13.8 P-23E Sect-13.8 P-24E Sect-13.8 P-25E Sect-13.8 P-26E Sect-13.8 P-27E Sect-13.8 P-28E Sect-13.8 P-29E Sect-13.8 P-30E Sect-13.8 P-31E Sect-13.8 P-32E Sect-13.8 P-33E Sect-13.8 P-34E Ch-13 P-1RE Ch-13 P-2RE Ch-13 P-3RE Ch-13 P-4RE Ch-13 P-5RE Ch-13 P-6RE Ch-13 P-7RE Ch-13 P-8RE Ch-13 P-9RE Ch-13 P-10RE Ch-13 P-11RE Ch-13 P-12RE Ch-13 P-13RE Ch-13 P-14RE Ch-13 P-15RE Ch-13 P-16RE Ch-13 P-17RE Ch-13 P-18RE Ch-13 P-19RE Ch-13 P-20RE Ch-13 P-21RE Ch-13 P-22RE Ch-13 P-23RE Ch-13 P-24RE Ch-13 P-25RE Ch-13 P-26RE Ch-13 P-27RE Ch-13 P-28RE Ch-13 P-29RE Ch-13 P-30RE Ch-13 P-31RE Ch-13 P-32RE Ch-13 P-33RE Ch-13 P-34RE Ch-13 P-35RE Ch-13 P-36RE Ch-13 P-37RE Ch-13 P-38RE Ch-13 P-39RE Ch-13 P-40RE Ch-13 P-41RE Ch-13 P-42RE Ch-13 P-43RE Ch-13 P-44RE Ch-13 P-45RE Ch-13 P-46RE Ch-13 P-47RE Ch-13 P-48RE Ch-13 P-49RE Ch-13 P-50RE Ch-13 P-51RE Ch-13 P-53RE Ch-13 P-54RE Ch-13 P-55RE Ch-13 P-1T Ch-13 P-2T Ch-13 P-3T Ch-13 P-4T Ch-13 P-5T Ch-13 P-6T Ch-13 P-7T Ch-13 P-8T Ch-13 P-9T Ch-13 P-10T Ch-13 P-11T Ch-13 P-12T Ch-13 P-13T Ch-13 P-14T Ch-13 P-15T Ch-13 P-16T

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MathMathematical Applications for the Management, Life, and Social Sciences11th Edition

Mathematical Applications for the ...

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Mathematical Applications for the Management, Life, and Social Sciences 11th Edition