Question 1185512
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How much money must you invest today in order to withdraw 1,000 pesos per year {{{highlight(at_the_beginnin_of_each_year)}}} for 10 years 
if interest rate is 12% {{{highlight(compounded_annually)}}} ?
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<pre>
Use the general formula  A = {{{W*p*((1-p^(-n))/r)}}}.


In this formula,  A is the deposited value (the unkown value in this problem);  

                  W  is the withdrawal annual rate W (1000 pesos per year at the biginning of each year);  

                  the annual compounding rate is  r = 0.12;  p = 1 + r = 1 + 0.12 = 1.12;   

                  n is the number of payment periods  n= 10  (10 years) 


From the formula


          A = {{{W*((p*(1-p^(-n)))/r))}}} = {{{1000*((1.12*((1-1.12^(-10))/0.12)))}}} = 6328.25  pesoss.         <U>ANSWER</U>


Notice that the TOTAL amount obtained from the account (1000 each year during 10 years) is  1000*10 = 10000 pesoss.


The difference  P10000 - P6328.25 = $3671.75  is the INTEREST earned by the account during 10 years.   


<U>ANSWER</U>.  The amount of money to be invested today is P6328.25.
</pre>

Solved.


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See my lessons in this site associated with annuity saving plans and retirement plans 


&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=http://www.algebra.com/algebra/homework/Sequences-and-series/Annuity-due-saving-plans-and-geometric-progressions.lesson>Annuity Due 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> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Withdrawing-a-certain-amount-of-money-periodically-from-a-compounded-saving-account.lesson>Withdrawing a certain amount of money periodically from a compounded saving account</A> (*)

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Solved-problems-on-Annuity-saving-plans.lesson>Miscellaneous problems on retirement plans</A> 


and especially lesson marked &nbsp;(*) &nbsp;in the list as the most relevant to the given problem.