Question 1135293
.


Let me re-formulate the problem, for clarity, in this way.


<pre>
    How much money should Sophie have ah her account at the beginning to withdraw  $15000 every month (at the beginning of each month)

    during 30 years, if her account earns 5% per year and is compounded semi-annually ?
</pre>


<U>Solution</U>


<pre>
It is the same and it works in the same way as if Sophia withdraws $15000*6 = $90000 at the beginning of every semi-annual period,
and the account is compounded semi-annually at 5% per year.


Use the general formula  X = {{{W*p*((1-p^(-n))/r)}}}.

In this case  the withdrawal semi-annual rate is W = $15000*6 = $90000,  the semi-annual compounding rate 
is  r = 0.05/2 = 0.025,  p = 1 + 0.025 = 1.025, the number of payment periods  is n = 30*2 = 60. So


          X = {{{90000*1.025*((1-1.025^(-60))/0.025)}}} = 2,851,324 dollars.     <U>ANSWER</U>


<U>ANSWER</U>.  To provide her goal, Sophie needs to have  $2,851,324  at the beginning at her account.
</pre>

Solved.


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See my lessons in this site associated with annuity saving plans and retirement plans 


&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>

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

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Solved-problem-on-Ordinary-Annuity-saving-plans.lesson>Solved problems on Ordinary Annuity saving plans</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Withdrawing-a-certain-amount-of-money-periodically-from-a-compounded-saving-account.lesson>Withdrawing a certain amount of money periodically from a compounded saving account</A> (*)

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Solved-problems-on-Annuity-saving-plans.lesson>Miscellaneous problems on retirement plans</A> 


and especially lesson marked (*) in the list as the most relevant to the given problem.