Question 1194565
.
Suppose you want to have $300,000 for retirement in 20 years. Your account earns 9% annual interest compounded monthly.
a) How much would you need to deposit in the account at the end of each month?
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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 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 = $300,000;  r = 0.09/12;  n = 20*12.  So, according to the formula (1), you get 
for the monthly payment 


    P = {{{300000*(((0.09/12))/((1+0.09/12)^(20*12)-1))}}} = $449.18.


<U>Answer</U>.  The necessary monthly deposit value is $449.18.
</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.