Question 1151734
.


I understand the problem in this way:


<pre>
    How much money should Susan deposit today in the morning to pay $1400 semiannually to her granddaughter 
    for 10 years starting from today at the afternoon for known goal ...

     . . . and so on . . . 
</pre>


<U>Solution</U>


<pre>
Use the general formula  X = {{{W*p*((1-p^(-n))/r)}}}.

In this case  the withdrawal semi-annual rate is W = $1400,  the semi-annual effective compounding rate 
is  r = 0.06/2 = 0.03,  p = 1 + 0.03 = 1.03, the number of payment periods  is n = 10*2 = 20. So


          X = {{{1400*1.03*((1-1.03^(-20))/0.03)}}} = 21,453.32 dollars.     <U>ANSWER</U>


<U>ANSWER</U>.  To provide her goal, Susan should deposit  $21,453.32 dollars today at this account.
</pre>

Solved.


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See my lessons in this site associated with annuity saving plans and retirement plans 


&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=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>

&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> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Withdrawing-a-certain-amount-of-money-periodically-from-a-compounded-saving-account.lesson>Withdrawing a certain amount of money periodically from a compounded saving account</A> (*)

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Solved-problems-on-Annuity-saving-plans.lesson>Miscellaneous problems on retirement plans</A> 


and especially lesson marked &nbsp;(*) &nbsp;in the list as the most relevant to the given problem.


These lessons contain all necessary theory, clear explanations and tens of examples.


Happy learning (!)