Question 1116001
.


            I will solve the problem in two steps.



<U>Step 1</U>.  &nbsp;Determine how much money &nbsp;"X" &nbsp;Heather must have in her account at the end of the first &nbsp;15-years period to get &nbsp;$650,000 
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;at the end of the 30 years period ?


<pre>
At this time interval, from 16-th year to 30-th year inclusively, the amount grows as an geometric progression with the common ratio of (1+0.11) = 1.11,

so <U>this formula</U> works at this time interval


    {{{X*1.11^15}}} = 650000,   which gives  X = {{{650000/1.11^15}}} = $135852.83.
</pre>


<U>Step 2</U>.  &nbsp;Determine a constant amount of money "Y" Heather must invest in her account at the end of each year 
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;of the first 15-years period to get &nbsp;$135852.83 &nbsp;at the end of this period ?


<pre>
At this time interval, from the 1-th year to 15-th year, the amount grows/accumulates as <U>ORDINARY ANNUITY SAVING PLAN</U> according the formula


    {{{Y*((1+0.11)^15-1)/0.11)}}} = 135852.83,   which gives  

    Y*34.40536 = 135852.83,  and then   Y = {{{135852.83/34.405356}}} = $3948.59.


<U>Answer</U>. The amount under the question is $3948.59.
</pre>

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On geometric progressions, &nbsp;see the introductory lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Geometric-progressions.lesson>Geometric progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/The-proofs-of-the-formulas-for-geometric-progressions.lesson>The proofs of the formulas for geometric progressions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Problems-on-geometric-progressions.lesson>Problems on geometric progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Word-problems-on-geometric-progressions.lesson>Word problems on geometric progressions</A>

in this site.


On Ordinary Annuity saving plan see the lesson

&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>

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic 
<U>"Geometric progressions"</U>.


Save the link to this textbook together with its description


Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson


into your archive and use when it is needed.