Question 1144002
.


            For me, the original text is some soup prepared using English words  (or something recalling English words), 
            but without a clear plan,  without an exact prescription and without knowledge of relevant terminology.


            Where did you take it ?   From your phone ?   Certainly,  not from a textbook.


            This soup is not a Math problem.  To get a status of a Math problem,  it must be edited and totally re-written.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;My editing is <U>THIS</U> :


<pre>
              Josie opened an account by depositing $5000 at the very beginning and then adding $500 regularly 
              at the end of every six months. The account is for 10 years and has the rate of 4.7% per annum 
              compounded semiannually. How much interest the account earns over this time?
</pre>


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;If you agree with my editing, then find my solution below.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;If you do not agree, &nbsp;then please let me know &nbsp;WHY.



<U>Solution</U>


<pre>
This account works as two separate saving plans:

    - one plan is the initial deposit of $5000 for 10 years at the rate of 4.7% per annum compounded semi-annually,  and

    - the other plan is an Ordinary Annuity for 10 years with regular deposits of $500 every six months at the rate 
      of 4.7% per annum compounded semi-annually


First account works according to the formula

    {{{FV[1]}}} = {{{5000*(1+0.047/2)^(2*10)}}}


Second account is Ordinary Annuity saving plan and works according the formula

    {{{FV[2]}}} = {{{500*(((1+0.047/2)^(2*10)-1)/((0.047/2)))}}}.


Calculate future value  {{{FV[1]}}}  and  future value  {{{FV[2]}}}, then add them and subtract (5000 + 2*500*10) = 15000 dollars 
that Josie deposited from the very beginning to the end in 10 years.


Then the expression  {{{FV[1]}}} + {{{FV[2]}}} - 15000  dollars will be your answer.
</pre>

----------------


On Ordinary annuity saving plans 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.