You'll be fine. I did my first century last month with very little training. Due to family and work, I was never really able to ride more than 35 miles at a time.
Plus due to weather, holidays and the flu, I only put in about 300 miles 2 1/2 months before the ride. I am 37 not 22. Also an organized ride really makes a century ride like half the distance. My 35 mile route riding solo was much more intense than the first 50 of the century. Lots of people to draft off of, which is what I did in the beginining. Finished 103 miles in 5:22 (ride time). It was an easy flat course. Just go for it, ride as much as possible until the week before the ride. Just remember to stay fueled up and hydrated. I did have cramping issues at the 75 mile mark.