agsin,
You might think of it like this: I've been a member of Moz since 2006, giving me one of the most aged profiles here in this forum, but for most of that time, I did not participate on the site, so my profile had like 10 or 20 points. In other words, up until the time I began participating, I had an old profile but I had no authority. The age doesn't really count for much--it's the engagement (points) that counts and which helps to adds authority.
Likewise, if your domain was registered back in 2006 but was not used until 2011, it would accrue age but not authority. Once the domain begins actively playing a role on the web and Google can measure that other domains and users are interacting with it, it may begin accruing authority.