It took me 13 months all told but I had a lot going on at the time. If your expenses are low you can do it in 8 months or so but that's unusual. Note that I say expenses and not income, it's usually best to pay as you go and not go into the red month to month.

That said, if you live somewhere with a convenient airport and a decent rental fleet (more places than you'd expect) it's highly liberating. I live near Denver and have gotten bored and flown to Canon city and surrounding areas for the day. Also, Pilots n Paws is awesome