0

Is there a way to solve the following for $g$?

$$ c\sum_{i=1}^{10}\frac{(1+g)^i}{(1+r)^i}=v $$

According to this there is no general easy answer as it is a 10th degree equation but I was still wondering if you could share some idea for this specific case. This might also be helpful.

Blue
  • 75,673
98418
  • 1
  • 3
    I think there's a geometric series in there somewhere. I'm too rusty to confirm it so someone else, take over please. – Sarvesh Ravichandran Iyer Jun 15 '22 at 10:29
  • 3
    While this can be simplified, using geometric series, that doesn't really make it solvable. Letting $\lambda = \frac {1+g}{1+r}$, your sum is $\lambda\times \frac {\lambda^{10}-1}{\lambda-1}$ so your equation becomes $c\lambda(\lambda^{10}-1) =\nu(\lambda-1)$ Or $c\lambda^{11}-(\nu+c)\lambda+\nu=0$ which, while, simpler looking, is still a pretty general degree $11$ polynomial. – lulu Jun 15 '22 at 11:11
  • 4
    What is the background of your question? Do you want a closed form of the solution? Or a way to find numerical approximations? I imagine that this is coming from finance? – mathcounterexamples.net Jun 15 '22 at 12:11

0 Answers0