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I need to understand how the compute the concave interpolation growth rate formule from a convex one. Formulas are based on a constant annual growth rate.
Convex interpolation formula:
r=[(X(t+n)/Xt )]^(1/n)-1
Then as a concave curve is just a convex one flipped twice, we just need to combine the following two equations (B is the upper limit to which the curve is converging in the long run and s is the researched growth rate):
Yt=B-xt
Yt=Y(t+n) [(1+s)]^n
to obtain
X(t+n)=Xt [1+((B-Xt)/Xt )(((1+s)^n-1)/(1+s)^n )]
As I only have the final step, I do not understand how to obtain the final equation from combining the two Yt.
Many thanks to the one which would help me
