Question 1139090
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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)}}},    


where  FV is the future value of the account;  P is the deposit at the beginning of each payment period (quarter, in this case) ; 
r is the quarterly percentage yield presented as a decimal; n is the number of deposits (= the number of the quarter periods, in this case).


2.5 years = 10 quarters.


From this formula, you get for for the monthly payment 


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


Under the given conditions, FV = $450,000;  r = 0.04/12;  n = 10.  So, according to the formula (1), you get for the monthly payment 


    P = {{{450000*(((0.068/4))/((1+0.068/4)*((1+0.068/4)^10-1)))}}} = $40967.39.


<U>Answer</U>.  The necessary quarterly deposit value is $40967.39.
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On Ordinary Annuity saving plans and Annuity Due 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>

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&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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