Question 1201794
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You put $159 per month in an investment plan that pays an APR of 5%. 
How much money will you have after 24 years? 
Compare this amount to the total amount of deposits made over the time period.
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        This problem is posed in a strange way, unprofessionally.

        To be professional, the problem should say whether the regular monthly payments 

        are made: at the beginning of each month or at the end of each month.

        Computational procedures are different in these cases, and the answers are different, too.


        In my solution, I will assume that the regular monthly payments of $159
        are made at the end of each month (ordinary annuity).



<pre>
Then it is a classic Ordinary Annuity saving plan. The general formula is 


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


where  FV is the future value of the account;  P is your 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).


Under the given conditions, P = 159;  r = 0.05/12;  n = 12*24 = 288.  
So, according to the formula (1), you get at the end of the 24-th year


    FV = {{{159*(((1+0.05/12)^288-1)/((0.05/12)))}}} =  $88,220.19.


Note that you the deposited amount is only  12*24*159 = $45,792.  The rest is what the account earns/accumulates in 24 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.