Unbroken Mitochondrial line?

[SamWatson]

the Mitochondrial Eve is the matrilineal most recent common ancestor of all currently living humans, her age is between 99 and 148 thousand years ago (Wkipedia).
First monkey lived 29 million years ago https://en.wikipedia.org/wiki/Monkey
Why do we have in the genes no mitochondria of the first monkey?

This question is a bit confused in several ways.
So yes, the mitochondria are not "in our genes", they are separate organelles in our cells carrying their own set of DNA, which is why they are preserved (up to mutations) from generation to generation along the female line of ancestors.
"The first monkey" is a bit of an arbitrary line drawn in the evolutionary tree. The first monkey in this sense is not necessarily the last common ancestor between humans and today's monkeys. But, that being said, the mitochondrial DNA of monkeys is more closely similar to ours than that of evolutionarily more distant animals, as one would expect. So there's no contradiction there. The fact that we have split away from them  a sum total of over 60 million years of evolutionary history ago (counting both branches) of course means that modern monkey mitochondria have drifted away from ours way more due to mutiations than have the different human mitochondria which are around today amongst each other. That's precisely because the human mitochondrial eve has lived relatively recently.

Human population have been studied. Now forget the human population. Apply same algorithms and DNA testers to the Monkey population. How old would be monkey-Eve?