Rerun - cumulative geometric returns over 20 periods

This is a repeat of something I did last year or the year before. I ran across it this week looking for something else and thought I'd throw it out there again.  This was a simulation of the expected value of the cumulative geometric return in each period over 20 periods. The arithmetic mean return expectation here is 7% with a standard deviation of 20%. That means we can estimate the expected geometric return at infinity with an imprecise estimator like EV(g) = A - V/2 or let's call it .05.  In this sim at the 20 period mark for this run the EV of geo return was ~.052.  The point of the chart below, however, is that all sorts of interesting things can happen between t=0 and t=∞ when it comes to: a) the rate of change of the expected value (mean), and b) the shape of any particular individual path, a path that a retiree, for example, might be presented with in his or her one run through life.  No wonder this ret-fin stuff is so hard.*

* As an amateur I realize that there are a few reasons one might qualify this kind of thing...lognormal this or that, etc. So, my advice? Don't read RH, read this instead.