Assuming that one's body remains constant throughout time travel, you would not age when you jumped to a different time. At least, that's how it is presented in sci-fi - the person steps into the machine, and pops out exactly the same in a different time.
Warning: reality might be quite different from stories that sell well. In which case, all bets are off. Relativity suggests that as a person approaches the speed of light, time slows down for that person, to where a one month journey for you the light speed traveler might be a 50 year time span for everyone else.
However, that's a one way trip. Relativity suggests you might be able to fast forward, but not rewind.
Note than in a lot of popular sci-fi, people don't travel at light speed, they instead warp space/time, so they avoid that paradox completely by just not physically traveling very far.
Oh no, I've gone crosseyed...