Question 1205773
.
Mr. Thompson wants to make monthly deposits into an annuity for his child 
so that $10,000 will be available in 8 years.  
If the interest rate is 8% compounded monthly, find the full deposit.
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<pre>
If the monthly deposits are made at the end of each month, then 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 monthly payment (deposit); 
r is the monthly percentage yield presented as a decimal; 
n is the number of deposits (= the number of years multiplied by 12, 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 = $10,000;  r = 0.08/12;  n = 8*12 = 96.  
So, according to the formula (1), you get for the monthly payment 


    P = {{{10000*(((0.08/12))/((1+0.08/12)^(8*12)-1))}}} = $74.70.


<U>Answer</U>.  The necessary monthly deposit value is $74.70.


Note that of projected $10,000, the total of the deposits will be only  8*12 times $74.70, 
i.e. 8*12*74.70 = 7171.20 dollars. The rest is what the account will earn/accumulate in 8 years.
</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.


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.



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To make such complicated calculations as they are in this problem,
you should have/use an appropriate calculator for such long formulas.


Ideal choice is MS Excel, if you have it in your computer.


Then you write a formula in a text editor, copy-paste it 
into an Excel work-sheet cell and click "enter" - the result is ready 
instantaneously.


If you have no MS Excel in your computer, you may find similar 
free of charge calculators in the Internet. One such calculator is


www.desmos.com/calculator


It allows you to do the same thing: you write a formula in a text editor, 
copy-paste it into this calculator and click "enter" - the result is ready 
instantaneously.