Question 1177395
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It is a classic Ordinary Annuity saving plan. The general formula is 


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


where  FV is the future value of the account;  P is the quarterly payment (deposit); 
r is the quarterly percentage yield presented as a decimal (it is " i " , in your terminology);
n is the number of deposits (= the number of years multiplied by 4, in this case).


Under the given conditions, P = 1000;  r = 0.07/4 = 0.0175;  n = 4*7 = 28.   <<<===---  it is partial answer to your questions 


So, according to the formula (1), you get at the end of the 7-th year


    FV = {{{1000*(((1+0.0175)^(4*7)-1)/0.0175)}}} = {{{1000*((1.0175^28-1)/0.0175)}}} = $35,737.88.


Note that you deposit only  4*7*$1000 = $28,000.  The rest is what the account earns/accumulates in 7 years.
</pre>

Solved, answered and explained.


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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.



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