Question 1201058
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you deposit $90 into an account at the beginning of each month.
The bank pays you 10% interest per year compounded monthly, at the end of nine years.
after 108 payments, how much will {{{highlight(cross(my))}}} <U>YOUR</U> account contain?
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<pre>
It is a classic Annuity Due saving plan. The general formula is 


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


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


Under the given conditions, P = 90 dollars;  r = 0.10/12;  n = 12*9 = 108 months.  
So, according to the formula (1), you will get at the end of the 9-th year


    FV = {{{90*(1+0.1/12)*(((1+0.1/12)^108-1)/(0.1/12))}}} = $15795.37  (rounded).


Note that you will deposit only  12*9*$90 = $9720 in 9 years.  
The rest is what the account earns/accumulates in 9 years.
</pre>

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On Annuity Due saving plans, &nbsp;see the lesson

&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>

in this site.


By some mysterious way, this Annuity Due saving plan has some relation to geometric progressions.


This referred lesson contains &nbsp;EVERYTHING &nbsp;you need to know about this subject, &nbsp;in clear and compact form.


Reading it, you will learn on how it does relate to geometric progressions, too.



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It is not for the first time this problem comes to the forum.


I just saw it once, &nbsp;probably, &nbsp;a month ago or so.


That time, &nbsp;exactly as today, &nbsp;it also came with this error &nbsp;" you deposit . . . " &nbsp;combined with &nbsp;" how much will my account contain ".



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;So, &nbsp;it systematically mixes &nbsp;" your deposit " &nbsp;and &nbsp;" my account ".



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Can you fix it in a way it would not repeated in the future ?