Withdrawal Rate and Investment Return

Here is the derivation of the withdrawal rate of a retirement portfolio. The value of the original portfolio is P, the initial withdrawal amount is x, the inflation rate is f_i, the real return rate is r_i, and the term is n.  The withdrawal amount is adjusted according to the inflation rate.

The withdrawal rate is x/P.  From the denominator, we can seen the effect of the real return, r₁ > r₂ > ... > r_n.
Withdrawal Rate