Difference between revisions of "022 Sample Final A, Problem 7"

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(Created page with "<span class="exam">Find the present value of the income stream <math style="vertical-align: -2px">Y = 20 + 30x</math> from now until 5 years from now, given an interest rate <...")
 
 
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|There isn't much to do here, except identify that <math style="vertical-align: -0.5px">T\,=\,5</math>, <math style="vertical-align: -5px">I(t)\,=\,20+30x</math> and the rate should be written as <math style="vertical-align: -1px">r\,=\,10%\,=\,0.10</math>.
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|There isn't much to do here, except identify that <math style="vertical-align: -0.2px">T\,=\,5</math>, <math style="vertical-align: -5px">I(t)\,=\,20+30x</math> and the rate should be written as <math style="vertical-align: -1px">r\,=\,10%\,=\,0.10</math>.
 
Click to the final answer to see them in the formula!
 
Click to the final answer to see them in the formula!
 
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::Present value = <math>\int_0 ^T I(t)e^{-rt}\,dt,\,=\,\int_0 ^5 (20+30x)e^{-0.10t}\,dt.</math>
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::Present value = <math>\int_0 ^T I(t)e^{-rt}\,dt\,=\,\int_0 ^5 (20+30x)e^{-0.10t}\,dt.</math>
  
 
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[[022_Sample_Final_A|'''<u>Return to Sample Exam</u>''']]
 
[[022_Sample_Final_A|'''<u>Return to Sample Exam</u>''']]

Latest revision as of 18:11, 6 June 2015

Find the present value of the income stream from now until 5 years from now, given an interest rate
(Note: Once you plug in the limits of integration, you are finished; you do not need to simplify our answer beyond that step.)

Foundations:  
The idea of an income stream is bit more complicated to set up than basic interest problems. We have two forces adjusting the balance of the account: the income stream, usually represented as , which represents the desired income to be withdrawn from the account, and the interest rate paid to the account. In order to evaluate this result, we use the formula
present value =
where is the time when our stream will run out, is the rate (compounded continuously) paid by the bank and is the desired continuous income stream.
Solution:  
There isn't much to do here, except identify that , and the rate should be written as .

Click to the final answer to see them in the formula!

Final Answer:  
Present value =

Return to Sample Exam