100 Hour Inspections

I was reading some FARs. Specifically, 91.409 section (b).

"(b) Except as provided in paragraph (c) of this section, no person may
operate an aircraft carrying any person (other than a crewmember) for hire,
and no person may give flight instruction for hire in an aircraft which that
person provides, unless within the preceding 100 hours of time in service the
aircraft has received an annual or 100-hour inspection and been approved for
return to service in accordance with part 43 of this chapter or has received
an inspection for the issuance of an airworthiness certificate in accordance
with part 21 of this chapter. The 100-hour limitation may be exceeded by not
more than 10 hours while en route to reach a place where the inspection can
be done. The excess time used to reach a place where the inspection can be
done must be included in computing the next 100 hours of time in service."

So let's say I get an Annual on my own plane in January, fly 100+ hours by
October, and then hire an instructor in November to get an IPC or a BFR. Have
I violated this FAR? Do I need get a 100 hour inspection or another annual
first?