Question 1204351
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You want to be able to withdraw the specified amount periodically from a payout annuity with the given terms. 
Find how much the account needs to hold to make this possible. Round your answer to the nearest dollar.
Regular withdrawal: $3400
Interest rate: 5%
Frequency monthly
Time: 28 years
what is the
Account balance: $
- i put 616750 and it was wrong
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        As this problem is presented in the post,  it uses many smart words,  but essentially,  it is incomplete.


                In other words,  the problem is posed   {{{highlight(highlight(unprofessionally))}}}.


        It is incomplete because it does not specify  WHEN  the withdrawal is made:  at the end or at the beginning of each month.


        Usually, in such problems, withdrawal is at the  BEGINNING  of each month to provide the living expenses;

        but in other problems,  it can be different.


        I solved the problem below under this assumption and got same value as in your post.



<pre>
The general formula  A = {{{W*p*((1-p^(-n))/r)}}}.


Here A is the initial amount at the account; W is the monthly withdrawn value (at the beginning of each month); 
r is the nominal monthly percentage r = 0.05/12 presented as a decimal;  
p = 1 + r  and n is the number of withdrawing periods (months, in this case).


In this problem,  W = 3400;  the monthly rate is  r = 0.05/12,  
p = 1 + 0.05/12, the number of payment periods (= the number of months) is n = 28*12 = 336.  So


          A = {{{3400*(1+0.05/12)*((1-(1+0.05/12)^(-336))/(0.05/12))}}} = 616749.88  dollars.


It is the initial amount.
</pre>


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;If to solve it at the different assumption &nbsp;(withdrawal is made at the END of each month), 
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;then the answer is &nbsp;614190.75  dollars.


Solved.


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In this site, &nbsp;there is a group of lessons associated with annuity saving plans and retirement plans.  &nbsp;They are


&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> 


From these lessons, &nbsp;you can learn the subject and can see many other similar solved problems.


The closest lesson to your problem is marked &nbsp;(*) &nbsp;in the list.