Question 1206598
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How much must be placed &nbsp;<U>at the end of</U> &nbsp;each month into a retirement account earning 12%
compounded monthly, if the value of the account is to reach $1,000,000 in 20 years
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I edited your post to make it sensical.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Find and read my editing for your post &nbsp;(underlined).



<pre>
This problem is to determine the amount of monthly payments/deposits.


Since the payments are at the end of each month, it is a classic Ordinary Annuity saving plan. 
The general formula to start (which is a PREREQUISITE and which you should know from your textbook) is 


    FV = {{{P*(((1+r)^n-1)/r)}}},    


where  FV is the future value of the account;  P is the monthly payment (deposit); 
r is the monthly effective percentage yield presented as a decimal; 
n is the number of deposits (= the number of years multiplied by 12, in this case).


From this formula, you get for the monthly payment 


    P = {{{FV*(r/((1+r)^n-1))}}}.     (1)


Under the given conditions, FV = $1,000,000;  r = 0.12/12 = 0.01;  n = 20*12 = 240.  
So, according to the formula (1), you get for the monthly payment 


    P = {{{1000000*(((0.12/12))/((1+0.12/12)^(20*12)-1))}}} = {{{1000000*(0.01/(1.01^240-1))}}} = $1010.87.


<U>Answer</U>.  The necessary monthly deposit is $1010.87.
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On Ordinary Annuity saving plans, &nbsp;see the lessons

&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=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>

in this site.


The lessons contain &nbsp;EVERYTHING &nbsp;you need to know about this subject, &nbsp;in clear and compact form.


When you learn from these lessons, &nbsp;you will be able to do similar calculations in semi-automatic mode.