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Question 923755: I have been pounding my head for 2 days trying to figure out the right equation for this problem and I am hoping someone here can help.
What is the amount a person would have to deposit today to be able to take out $5000 a year for 10 years from an account earning 8 percent annually?
Thanks!
Found 2 solutions by josgarithmetic, KMST:
Answer by josgarithmetic(39630)   (Show Source):
You can put this solution on YOUR website! p, amount to deposit today.
YEAR_________________BAL
0___________________p(1.08)^0
1___________________p(1.08)^1
2___________________p(1.08)^2
y___________________p(1.08)^y
Your question asks,  to find p.
Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website! The way I understand it you want to know how much money should be deposited at time = 0 years,
into an account earning 8 percent annually,
so that at t=1 year, t=2 years, ..., t=8 years,
there would be at least $5000 that can be taken out.
At  ,  .
At  (at the end of the first year) 8% interest (  is added to the balance,
bringing the balance up to  ,
and immediately,  is taken out,
bringing the balance down to 
At  ,  is again
increased by a factor of  ,
and reduced by the withdrawal of , so
 .
At  ,  is again
increased by a factor of ,
and reduced by the withdrawal of , so
 .
This pattern repeats every year, and
at  ,
If at that point  ,
NOTE:
The sum 
is the sum of a geometric sequence with ratio .
You may know a formula for that, but otherwise you can see that
 , and then
 ---> --->
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