Question 1187349
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How much must you deposit at the end of each of the next 12 years in a savings account paying 10% annually 
in order to have $1 million saved by the end of those 12 years?
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<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 annual payment (deposit); r is the annual percentage yield presented as a decimal; 
n is the number of deposits (= the number of years, in this case).


From this formula, you get for for the annual payment 


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


Under the given conditions, FV = $1,000,000;  r = 0.1;  n = 12.  So, according to the formula (1), you get for the annual payment 


    P = {{{1000000*(0.1/((1+0.1)^12-1))}}} = $46,763.32.


<U>Answer</U>.  The necessary annual deposit value is $46,763.32.


Note that of projected $1,000,000 the total, you will deposits only  10 times $46,763.32, i.e. 10*46,763.32 = 467633.2 dollars.
The rest is what the account will earn/accumulate/accrue in 10 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.