SOLUTION: 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

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(39618) (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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