Question 1133083
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Terry's mother figures that she will need to have $200 000 at the end of 10 years. 
The retirement fund that she has chosen earns {{{highlight(annual)}}} interest at 6% compounded semi-annually.

A) How much does she need to invest in the fund every six months?

B) how much interest will Terry's mother have earned over the course of her investment?
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Pay attention on how I edited your post to make it <U>precisely correct</U>.



<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 semi-annual payment (deposit); r is the semi-annual percentage yield presented as a decimal; 
n is the number of deposits (= the number of years multiplied by 2, in this case).


From this formula, you get for the semi-annual payment 


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


Under the given conditions, FV = $200,000;  r = 0.06/2;  n = 10*2 = 20.  So, according to the formula (1), you get for the semi-annual payment 


    P = {{{200000*(((0.06/2))/((1+0.06/2)^(10*2)-1)))}}} = $7443.14.


<U>Answer to question (A)</U> :    The necessary semi-annual deposit value is $7443.14.



Note that of projected $200,000 the total of mother's deposits will be only  10*2 times $7443.14, i.e. 10*2*7443.14 = 148862.80 dollars.


<U>Answer to question (B)</U> :  The interest mother will have earned over the course of her investment is  {{{(200000 - 148862.80)/148862.80}}} = 34.35%.    
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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.


The lessons contain &nbsp;EVERYTHING &nbsp;you need to know about this subject, &nbsp;in clear and compact form.


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