Question 1205569
.
You can purchase an investment that pays $75,000 at the beginning of each year for twenty years. 
Similar investments earn an 8% interest rate. How much will the payments be worth to you 
at the end of fifteen years?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
Similar account at the end of fifteen years is able to provide payments of $75,000 
at the beginning of each year for 5 (five) years.


So, the question is: find the amount, which, when invested at 8% annual interest rate,
will provide payment (withdrawing) $75,000 at the beginning of each year for five years.


    +----------------------------------------------+
    |    It is a standard question/problem about   |
    |      a starting amount of a sinking fund.    |
    +----------------------------------------------+


The general formula  to calculate the starting amount at the account is

    X = {{{W*p*((1-p^(-n))/r)}}}.


In this formula, W is  the regular annual withdrawal, W = $75000;  the factual annual compounding rate 
is  r = 0.08,  p = 1 + 0.08 = 1.08, and the number of payment periods  is n = 5 years. So


          X = {{{75000*1.08*((1-1.08^(-5))/0.08)}}} = 323409.52 dollars.     


It is the  <U>ANSWER</U>  to the problem's question.
</pre>

Solved.


--------------


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.