The fun is in the journey. Try soaring. You can get your private ticket for under $5k and power later as an add on. When the thermals are working you can stay up all day, all on a 2.5 gallons for the tow plane.
Your math is OK, your assumptions are not. The $9,900 includes unlimited ground and flight instruction, unlimited simulator usage, all materials and flight test fees, and the whatever hours it takes in the aircraft.
And the price is guaranteed.
That's fair. And an interesting pitch, taking much of the risk out for the student.
I guess I'm still suffering from sticker shock at $10k for a Private. But that just proves I'm old.