Question 1147891
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It is a classic Ordinary Annuity saving plan. The general formula is 


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


where  FV is the future value of the account;  P is the quarterly payment (deposit); r is the effective quarterly rate yield 
presented as a decimal; n is the number of deposits (= the number of quarters in 2.5 years, i.e. 10, in this case).


From this formula, you get for the quartely payment 


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


Under the given conditions, FV = $31,000;  r = 0.05/4;  n = 10.  So, according to the formula (1), you get for the monthly payment 


    P = {{{31000*(((0.05/4))/((1+0.05/4)^10-1)))}}} = $2929.60.


<U>Answer</U>.  The necessary monthly deposit value is $2929.60.
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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>

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