Answer
Yes, the stock did undergo simple interest changes in the given period.
Work Step by Step
The given graph is a graph of stock value (FV) in time (t).
$INT=PVrt$,
$FV-PV=PVrt$,
$FV=PVrt+PV$,
PV is constant (the stock price in January)
IF r is constant, then
$FV$, as a function of time, is a linear function
(with PV as y-intercept and $PV\cdot r$ as slope).
The graph given by the problem is clearly not linear in the given period,
So, r is not a constant,
r is also a function of time (changes with time).
Yes, the stock did undergo simple interest changes in the given period.