Question 1201661
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Three friends want $3,000,000 at the end of 10 years. How much money
should they put into an account each month that pays 7% annual interest
compounded monthly?
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<pre>
If the deposit is made regularly at the end of each month, such saving plan is called 
an Ordinary Annuity. The general formula for such a plan 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 = $3,000,000;  r = 0.07/12;  n = 10*12 = 120.  
So, according to the formula (1), you get for the monthly payment 


    P = {{{3000000*(((0.07/12))/((1+0.07/12)^(10*12)-1))}}} = $17,332.55.


<U>Answer</U>.  The necessary monthly deposit value is $17,332.55.


Note that of projected $3,000,000, the total of deposits will be only  10*12 times $17,332.55, 
i.e. about 10*12*17332.55 = 2079906 dollars. The rest is what the account will earn/accumulate in 10 years.
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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.