Solving Equations with Summations of X: Help Needed!

[ghehir]

Hi All,

I am having trouble solving an equation for X because the equation has summations of the X value to a power. Can anybody help me find the best way to solve this type of equation. I have included a simple example of what I mean below:

20
E {const/[(1+X)^t]} = const
t=4

Do you know if this can be simplified or if you can get the x on its own?

Thanks a million for any help with this..

Regards,

Gary

 

[HallsofIvy]

$$\sum_{t=4}^{20} \frac{C}{(1+x)^t}= C$$
Is that your equation? You can factor that "C" out and cancel:
$$\sum_{t=4}^{20}\frac{1}{(1+x)^t}= 1$$

That's a "geometric series". The geometric series $$\sum_{t=0}^n r^t= \frac{1- r^{n+1}}{1- r}$$ as long as |r|< 1. Here r= 1/(1+x). Also since your sum starts at 4 rather than 0, you should use that formula with n= 20 and 3 and subtract to get a "closed form" equation.

 

[ghehir]

Hi,

Thanks for your reply but I had the equation in wrong. I tried to simplify the equation I am working with in order to post it. This is closer to what I need, I can get values for everything except Z and I was wondering if it was possible to get the equation in the form of Z = ...
4 20
V = E {(Xt.Yt)/[(1+Z+3%)^t]} + E {X4.Y4.(D)/[(1+Z+3%)^t]} + ...
t=0 t=4


... [1/(1+Z+3%)^t].(X20.Yo/z+3%-I)