SOLUTION: Hey I'm just so lost, my older sister tried helping me but she can't remember what to do. I would greatly appreciate your help! (I also greatly NEED it) hahaa By the way I'm not su

Algebra ->  Probability-and-statistics -> SOLUTION: Hey I'm just so lost, my older sister tried helping me but she can't remember what to do. I would greatly appreciate your help! (I also greatly NEED it) hahaa By the way I'm not su      Log On


   



Question 580458: Hey I'm just so lost, my older sister tried helping me but she can't remember what to do. I would greatly appreciate your help! (I also greatly NEED it) hahaa By the way I'm not sure if I picked the right topic...but I tried. anyways it's bookwork it says:
Mrs.Boyko has a trust fund from which she withdraws 5% each year. If the fund has a value of $50,000 this year, what will be the value of the fund after 10 years?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
This is the right place ( unless I'm in the wrong place )
I will say: +x+=+50000+
After 1 yr she will have:
+x+-+.05x+
After 2 yrs she will have
+x+-+.05x+-+%28+.05%2A%28+x+-+.05x+%29+%29+
After 3 yrs she will have:

----------
A little too complicated. Go back to the 2nd step
and factor out +x+-+.05x+
+x+-+.05x+-+%28+.05%2A%28+x+-+.05x+%29+%29+=+%28+x+-+.05x+%29+%2A+%28+1+-+.05+%29+
and ++%28+x+-+.05x+%29+%2A+%28+1+-+.05+%29+=+x%2A%28+1+-+.05+%29%2A%28+1+-+.05+%29+
and +x%2A%28+1+-+.05+%29%2A%28+1+-+.05+%29+=+x%2A%28+1+-+.05+%29%5E2+
A lot better
Now plug this into step 3 where you see +x+-+.05x+-+%28+.05%2A%28+x+-+.05x+%29+%29+

++x%2A%28+1+-+.05+%29%5E2+-+.05%2A%28++x%2A%28+1+-+.05+%29%5E2+%29+
This time factor out ++x%2A%28+1+-+.05+%29%5E2+
+x%2A%28+1+-+.05+%29%5E2+%2A+%28+1+-+.05+%29+
+x%2A%28+1+-+.05+%29%5E3+
-------------------
This is the rule. If you start with +x+ dollars and take out 5%
each year, +x%2A%28+1+-+.05+%29%5En+, after n years, this is what you
have left, so after 10 yrs,
+50000%2A%28++1+-+.05+%29%5E10+
+50000%2A%28.95%29%5E10+
+50000%2A.598737+
+29936.847+
In 10 yrs, the value of the fund is $29,936.85