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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

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BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

Suppose that a printing firm considers its production as a continuous income stream. If the annual rate of flow at time t is given by

f ( t ) = 97.5 e 0.2 ( t + 3 ) in thousands of dollars per year and money is worth 6 % compounded continuously, find the present value and future value of the presses over the next 10 years.

To determine

To calculate: The present value and future value of the printing press whose income stream for next 10 years from 6% compounded continuously income stream is approximated by f(t)=97.5e0.2(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 printing press whose income stream for next 10 years from 6% compounded continuously income stream is approximated by f(t)=97.5e0.2(t+3) thousands dollars per year. Whereby, t is the rate of flow at 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)ertdt.

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=erk0kf(t)ertdt.

Calculation:

Consider the income equation:

f(t)=97.5e0.2(t+3)

Since, the income to be calculated for next 10 years:

Thus,

k=10

And

Money is worth 6% compounded continuously,

Thus,

r=0.06

Considering the formula:

Present value=0kf(t)ertdt

Substituting 10 for k, 0.06 for r and 97.5e0.2(t+3) for f(t) to get:

Present Value=01097.5e0.2(t+3).e0.06tdt=97.5010e0.26t0.6dt=[97.50.26e0.26t0.6]010

Solving the limit of the function to get:

Present Value=[97.50.26e0.26(10)0.6][97.50.26e0

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Chapter 13 Solutions

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Sect-13.1 P-9ESect-13.1 P-10ESect-13.1 P-11ESect-13.1 P-12ESect-13.1 P-13ESect-13.1 P-14ESect-13.1 P-15ESect-13.1 P-16ESect-13.1 P-17ESect-13.1 P-18ESect-13.1 P-19ESect-13.1 P-20ESect-13.1 P-21ESect-13.1 P-22ESect-13.1 P-23ESect-13.1 P-24ESect-13.1 P-25ESect-13.1 P-26ESect-13.1 P-27ESect-13.1 P-28ESect-13.1 P-29ESect-13.1 P-30ESect-13.1 P-31ESect-13.1 P-32ESect-13.1 P-33ESect-13.1 P-34ESect-13.1 P-35ESect-13.1 P-36ESect-13.1 P-37ESect-13.1 P-38ESect-13.1 P-39ESect-13.1 P-40ESect-13.2 P-1CPSect-13.2 P-2CPSect-13.2 P-1ESect-13.2 P-2ESect-13.2 P-3ESect-13.2 P-4ESect-13.2 P-5ESect-13.2 P-6ESect-13.2 P-9ESect-13.2 P-10ESect-13.2 P-11ESect-13.2 P-12ESect-13.2 P-7ESect-13.2 P-8ESect-13.2 P-23ESect-13.2 P-24ESect-13.2 P-13ESect-13.2 P-14ESect-13.2 P-15ESect-13.2 P-16ESect-13.2 P-17ESect-13.2 P-18ESect-13.2 P-19ESect-13.2 P-20ESect-13.2 P-21ESect-13.2 P-22ESect-13.2 P-25ESect-13.2 P-26ESect-13.2 P-27ESect-13.2 P-28ESect-13.2 P-29ESect-13.2 P-30ESect-13.2 P-31ESect-13.2 P-32ESect-13.2 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P-2ESect-13.8 P-3ESect-13.8 P-4ESect-13.8 P-5ESect-13.8 P-6ESect-13.8 P-7ESect-13.8 P-8ESect-13.8 P-9ESect-13.8 P-10ESect-13.8 P-11ESect-13.8 P-12ESect-13.8 P-13ESect-13.8 P-14ESect-13.8 P-15ESect-13.8 P-16ESect-13.8 P-17ESect-13.8 P-18ESect-13.8 P-19ESect-13.8 P-20ESect-13.8 P-21ESect-13.8 P-22ESect-13.8 P-23ESect-13.8 P-24ESect-13.8 P-25ESect-13.8 P-26ESect-13.8 P-27ESect-13.8 P-28ESect-13.8 P-29ESect-13.8 P-30ESect-13.8 P-31ESect-13.8 P-32ESect-13.8 P-33ESect-13.8 P-34ECh-13 P-1RECh-13 P-2RECh-13 P-3RECh-13 P-4RECh-13 P-5RECh-13 P-6RECh-13 P-7RECh-13 P-8RECh-13 P-9RECh-13 P-10RECh-13 P-11RECh-13 P-12RECh-13 P-13RECh-13 P-14RECh-13 P-15RECh-13 P-16RECh-13 P-17RECh-13 P-18RECh-13 P-19RECh-13 P-20RECh-13 P-21RECh-13 P-22RECh-13 P-23RECh-13 P-24RECh-13 P-25RECh-13 P-26RECh-13 P-27RECh-13 P-28RECh-13 P-29RECh-13 P-30RECh-13 P-31RECh-13 P-32RECh-13 P-33RECh-13 P-34RECh-13 P-35RECh-13 P-36RECh-13 P-37RECh-13 P-38RECh-13 P-39RECh-13 P-40RECh-13 P-41RECh-13 P-42RECh-13 P-43RECh-13 P-44RECh-13 P-45RECh-13 P-46RECh-13 P-47RECh-13 P-48RECh-13 P-49RECh-13 P-50RECh-13 P-51RECh-13 P-53RECh-13 P-54RECh-13 P-55RECh-13 P-1TCh-13 P-2TCh-13 P-3TCh-13 P-4TCh-13 P-5TCh-13 P-6TCh-13 P-7TCh-13 P-8TCh-13 P-9TCh-13 P-10TCh-13 P-11TCh-13 P-12TCh-13 P-13TCh-13 P-14TCh-13 P-15TCh-13 P-16T

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