Question 1153017
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            I will assume that withdrawing is made at the beginning of each year and that the compounding is made annually 
            at the end of each year.


            By the way,  these details are  IMPORTANT  and should go as a part of the problem formulation. 



<pre>
The general formula  in this case is  X = {{{W*p*((1-p^(-n))/r)}}}.

Here W = $40000 is the amount to withdraw at the beginning of each year;  r = 0.08 is the annual interest rate,  

p = 1 + 0.08 = 1.08;  n is the number of payment periods (number of years, which is  25  in this case),

X is the starting amount at the account (the value under the question). 


So

          X = {{{40000*1.08*((1-1.08^(-25))/0.08)}}} = 461,150.33 dollars.     <U>ANSWER</U>


<U>ANSWER</U>.  To provide you goal, you need to have  $461,150.33  at the beginning at your 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 &nbsp;(*) &nbsp;in the list as the most relevant to the given problem.