A continuous income stream has an annual rate of flow at time t given by f ( t ) = 9000 e 0.12 t (dollars per year) Find the present value of this income stream for the next 10 years if money is worth 6 % compounded continuously.

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To determine To calculate: The present value of the income stream for next 10 years from 6 % compounded continuously income stream is approximated by f ( t ) = 9000 e 0.12 t dollars per year. Whereby, t is the rate of flow at time yearly. Explanation Given Information: The present value of the income stream for next 10 year from 6 % compounded continuously income stream is approximated by f ( t ) = 9000 e 0.12 t dollars per year. Whereby, t is the rate of flow at time is 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 = ∫ 0 k f ( t ) e − r t d t . Calculation: Consider the income equation: f ( t ) = 9000 e 0.12 t Since, the income to be calculated for next 10 years: So, the value of k can be determine as: k = 10 And Money is worth 6 % compounded continuously, Thus, r = 0.06 Considering the formula: Present Value = ∫ 0 k f ( t ) e − r t d t Substituting 10 for k , 0.06 for r and 9000 e 0.12 t for f ( t ) to get: Present Value = ∫ 0 10 9000 e 0

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Mathematical Applications for the ...

12th Edition

Ronald J. Harshbarger + 1 other

Publisher: Cengage Learning

ISBN: 9781337625340

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BuyFind

Mathematical Applications for the ...

12th Edition

Ronald J. Harshbarger + 1 other

Publisher: Cengage Learning

ISBN: 9781337625340

Solutions

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Answer 3

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Answer 4

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Answer 5

To determine

To calculate: The present value of the income stream for next 10 years from 6% compounded continuously income stream is approximated by f(t)=9000e0.12t dollars per year. Whereby, t is the rate of flow at time yearly.

Explanation of Solution

Given Information:

The present value of the income stream for next 10 year from 6% compounded continuously income stream is approximated by f(t)=9000e0.12t dollars per year. Whereby, t is the rate of flow at time is 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.

Calculation:

Consider the income equation:

f(t)=9000e0.12t

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

So, the value of k can be determine as:

k=10

And

Money is worth 6% compounded continuously,

Thus, r=0.06

Considering the formula:

Present Value=∫0kf(t)e−rtdt

Substituting 10 for k, 0.06 for r and 9000e0.12t for f(t) to get:

Present Value=∫0109000e0

A continuous income stream has an annual rate of flow at time t given by f ( t ) = 9000 e 0.12 t (dollars per year) Find the present value of this income stream for the next 10 years if money is worth 6 % compounded continuously.

Mathematical Applications for the ...

Solutions

Mathematical Applications for the ...

A continuous income stream has an annual rate of flow at time t given by f ( t ) = 9000 e 0.12 t

(dollars per year)

Find the present value of this income stream for the next 10 years if money is worth 6 % compounded continuously.

Explanation of Solution

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