Question 1172747
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Paul and Donna Kelsch are planning a Mediterranean cruise in 3 years and will need $9,500 for the trip. 
They decide to set up a "sinking fund" savings account for the vacation. They intend to make regular payments 
at the end of each 3 month period into the account that pays 6% interest compounded quarterly. 
What periodic sinking fund payment (in $) will allow them to achieve their vacation goal? (Round your answer to the nearest cent.)
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<pre>
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 factual quarterly rate presented as a decimal; 
       n is the number of deposits (= the number of years multiplied by 4, in this case).


From this formula, you get for the monthly payment 


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


Under the given conditions, FV = $9,500;  r = 0.06/4;  n = 3*4.  So, according to the formula (1), 
you get for the quarterly payment 


    P = {{{9500*(((0.06/4))/((1+0.06/4)^(3*4)-1)))}}} = $728.46.


<U>Answer</U>.  The necessary quarterly deposit value is $728.46.
</pre>

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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.


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When you learn from these lessons, &nbsp;you will be able to do similar calculations in semi-automatic mode.