Question 1122484
.
Suppose you want to have $800,000 for retirement in 30 years. Your account earns 8% interest.

a) How much would you need to deposit in the account each month?

$


b) How much interest will you earn?

$
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To be consistent, the condition should be edited in this way:


<pre>
    Suppose you want to have $800,000 for retirement in 30 years. Your account <U>is compounded monthly and</U> earns 8% <U>annual</U> interest.
</pre>


Then the solution is <U>THIS</U> :


<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 = $800,000;  r = 0.08/12;  n = 30*12.  So, according to the formula (1), the monthly payment is


    P = {{{800000*(((0.08/12))/((1+0.08/12)^(30*12)-1)))}}} = $536.78.


<U>Answer</U>.  a)  <U>How much would you need to deposit in the account each month ?</U> - $536.78.


            Note that of projected $800,000 the total you deposit will be only  30*12 times $536.78, i.e. about 30*12*536.78 = 193241 dollars.                     
            The rest is what the account will earn/accumulate in 30 years.


         b)  <U>How much interest will you earn ?</U>  - You will earn {{{((800000-193241)/193241)*100}}} = 314%  of interest.
</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.