Question 1151380
.
<pre>

It works in this way:  they withdraw $12000 at the beginning of every quarter, and the account is compounded quarterly 
at the nominal rate of 8% per year.


The general formula  to calculate the starting amount at the account is

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


In this formula, W is  the regular withdrawal per quarter, W = $12000;  the factual quarterly compounding rate 
is  r = 0.08/4 = 0.02,  p = 1 + 0.02 = 1.02, and the number of payment periods  is n = 30 years * 4 quarters = 120. So


          X = {{{12000*1.02*((1-1.02^(-120))/0.02)}}} = 555,149.96 dollars.     It is the  <U>ANSWER</U>  to the problem's question [1].


The answer to question [2] is  {{{555149.96/(30*4*12000)}}} = 0.39 dollars.


The answer to question [3] is 30*4*12000 = 1,440,000 dollars.


Regarding question [4], I do not understand precisely its meaning.
</pre>

Solved.


--------------


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.