Question 1113633
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I will interpret the condition in this way:


<pre>
    1)  We have first the period of &nbsp;&nbsp;{{{4015/365}}} = 11 years, &nbsp;when the initial deposit of X dollars grows at &nbsp;8% &nbsp;compounded semiannually.


    2)  Then the second period starts, &nbsp;when the company withdraw &nbsp;$17900 semiannually for &nbsp;12 years to fulfill its obligation to Robert.

        During this period of &nbsp;12 years the rest of the account is still compounded at &nbsp;8% semiannually, 
        and at the end of the &nbsp;12 years period the amount vanishes.
</pre>

The condition does not formulate all these details, &nbsp;so, &nbsp;from one side, &nbsp;it is my own interpretation / (fantasy).


From the other side, &nbsp;only this interpretation makes the problem really interesting, &nbsp;and it is major reason, &nbsp;why I start to work on it.



<U>Solution</U>


<pre>
1.  After 11 years, the initial deposit of X dollars becomes

    P = {{{X*(1+0.08/2)^(2*11)}}} = {{{X*1.04^22}}}.



2.  Then the following next 12 years period we have the ordinary annuity plane with the NEGATIVE semiannual deposit (= withdraw) of $17900.

    So, the usual ORDINARY ANNUITY PLAN formula works with the negative deposit of 17900 dollars:

   
    P = {{{17900*(1-(1-0.08/2)^(2*12))/(0.08/2)}}} = {{{(17900*(1-0.96^24))/0.04}}}.


    So your equation to find X is THIS:


       {{{X*1.04^22}}} = {{{17900*((1-0.96^24)/0.04)}}}.


       x*2.369919 = 279502.6  =====>  X = {{{279502.6/2.369919}}} = 117937.60.


<U>Answer</U>.  Under the given condition and interpretation the initial deposit the company must make TODAY is  117937.60 dollars.
</pre>

Solved.


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See the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Ordinary-Annuity-saving-plans-and-geometric-progressions.lesson>Ordinary Annuity saving plans and geometric progressions</A>

in this site.


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I absolutely agree with John in that you do not need copy your post many times - it only annoys/irritates the tutors and works against your best interests.