Question 1198679
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Jane Adele deposits $1,300 in an account at the beginning of each 3-month period for 12 years. 
If the account pays interest at the rate of 4%, compounded quarterly, 
how much will she have in her account after 12 years?
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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 quarterly payment (deposit) 
at the beginning of each payment period; r is the quarterly percentage yield presented as a decimal; 
n is the number of deposits (= the number of years multiplied by 4, in this case).


Under the given conditions, P = 1300;  r = 0.04/4 = 0.01;  n = 12*4 = 48.  
So, according to the formula (1), Jane Adele will get at the end of the 4-th year


    FV = {{{1300*(1+0.01)*(((1+0.01)^48-1)/0.01)}}} =  {{{1300*1.01*((1.01^48-1)/0.01)}}} = $80385.28  (rounded).


Note that Jane Adele will deposit only  12*4*$1300 = $62400 in 12 years.  
The rest is what the account earns/accumulates in 12 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>

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