Will a domain that is fifteen years old with no backlinks rank higher in Google than a 6 month old domain name with no backlinks?
Let's take keywords in domain out of the equation and they would both be the same extension.
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Age of domain is a huge trust factor for a domain. It is important.
However, as Simon Hayter alludes to, there is more complication to this than just the domain age. For example, when the domain is transferred and the registration information changes, the domain age no longer matters. The domain age, in effect, actually resets within Google.
The trust was earned by the previous owner and not by the new owner. It is not uncommon for a domain name to be snatched-up by a monetizer that then flogs the boggie-snots out of any value the domain has until it is completely leached into the soil then sells the domain name to some poor schlub that pay thousands of dollars for the privilege of buying excrement.
Okay. That was a bit colorful. Hopefully humorous too. However, I think I made my point. Right??
The length of time a domain has been registered, and up and running, does help with SEO but, as the saying goes, content is king and it is your content that will determine your rank going forward. Length of time of the domain name is only a brownie point.