Answer
No, the text does not describe simple interest growth.
Work Step by Step
Simple interest growth complies with
$FV=PV(1+rt)$.
PV is (always) the initial amount.
So, after 1 year, taking 100 units as PV, FV should be
$FV=PV(1+0.1\times 1)=100\cdot 1.01=101$ units
After 2 years,
$FV=PV(1+0.1\times 2)=100\cdot 1.02=102$ units.
The problem text, however, does not take PV to be the initial PV,
but the FV of the year before, and t is again t=1:
Again, taking 100 units as PV:
After one year,
$FV=PV(1+0.1\times 1)=100\cdot 1.01=101$ units
After 2 years, they take PV=101
$FV=PV(1+0.1\times 1)=101\cdot 1.01=1.0201$ units.
So, no, the text does not describe simple interest growth.
