Question 1178719
.
What is the present worth of a P250 annuity starting at the end of the third year 
and continuing to the end of the fourth year, if the annual interest rate is 5%? 
With cash flow diagram.
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I will use slightly different logic comparing with @CPhill.



<pre>
The cash flow diagram


Years     1      2      3       4   

Deposits  0      0     250     250

Amount    0      0     250     250 + 0.05*250 + 250 = 512.50.

                       end     end        
                       of the  of the
                       year    year


In this problem, the amount at the account is P250 at the end of the 3rd year 
(after first depositing), and it is not a subject of compounding at the end of the year 3.


First compounding will happen at the end of the 4th year, and immediately after that 
the next amount of P250 will be deposited, giving the total at the end of year 4 as 
250 + 0.05*250 + 250 = 512.50.


So, at the end of the 4th year, after first compounding and the second deposit, 
the amount at the account is 512.50.


To get the present value for "now", which is the beginning of the year 1, we should rewind 
this amount of P512.50 4 (four) years back.


So, the present value is  {{{512.50/(1+0.05)^4}}} = {{{512.50/1.05^4}}} = P421.64  (rounded).


<U>ANSWER</U>.  The present value is  P421.64  (rounded).
</pre>

Solved.



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Below is my comment to Edwin's post.


Edwin, I did not get, to which address did you directed/targeted your post - to mine or 
to the address of @CPhill, who solves here old problems one after another in numbers of hundreds ?


Edwin, you see students everywhere.  


Stop, your students are a myth, they are mythical.


Just starting from the year 2021 we all at this forum work almost exclusively 
for AI (= Artificial Intelligence), without knowing it, without understanding it 
and without even suspecting it.


In the school, nobody will give such problem to a student, because it is one level above the school level.


Also, after posting a problem and responding a solution, this solution is viewed by others 15 times
in the archive, according to the statistic.


So, your notice is interesting, but irrelevant to the process of functioning of this forum.


Have a nice day !