MathAdmin at 01:11, 7 June 2015

2015-06-07T01:11:41Z

MathAdmin: Created page with "Find the present value of the income stream $Y = 20 + 30x$ from now until 5 years from now, given an interest rate <..."

2015-06-06T04:36:33Z

Created page with "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 <..."

New page

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 <math style="vertical-align: -1px">r = 10%.</math>
 
''(Note: Once you plug in the limits of integration, you are finished; you do not need to simplify our answer beyond that step.)''

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!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 <math style="vertical-align: -5px">I(t)</math>, which represents the desired income to be withdrawn from the account, and the interest rate paid to the account.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 = <math>\int_0 ^T I(t)e^{-rt}\,dt,</math>
|-
|where <math style="vertical-align: 0px">T</math> is the time when our stream will run out, <math style="vertical-align: 0px">r</math> is the rate (compounded continuously) paid by the bank and <math style="vertical-align: -5px">I(t)</math> is the desired continuous income stream.
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!Solution:  
|-
|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>.
Click to the final answer to see them in the formula!
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!Final Answer:  
|-
|
::Present value = <math>\int_0 ^T I(t)e^{-rt}\,dt,\,=\,\int_0 ^5 (20+30x)e^{-0.10t}\,dt.</math>

|}

[[022_Sample_Final_A|'''Return to Sample Exam''']]

@@ Line 17: / Line 17: @@
 !Solution: &nbsp;
 |-
-|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>.
+|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!
 |}
@@ Line 25: / Line 25: @@
 |-
+|
-::Present value = <math>\int_0 ^T I(t)e^{-rt}\,dt,\,=\,\int_0 ^5 (20+30x)e^{-0.10t}\,dt.</math>
+::Present value = <math>\int_0 ^T I(t)e^{-rt}\,dt\,=\,\int_0 ^5 (20+30x)e^{-0.10t}\,dt.</math>
 |}
 [[022_Sample_Final_A|'''<u>Return to Sample Exam</u>''']]

022 Sample Final A, Problem 7 - Revision history

MathAdmin at 01:11, 7 June 2015

MathAdmin: Created page with "Find the present value of the income stream Y = 20 + 30x from now until 5 years from now, given an interest rate <..."

MathAdmin: Created page with "Find the present value of the income stream $Y = 20 + 30x$ from now until 5 years from now, given an interest rate <..."