#confession dial

The Doctor (at least the 12th one) has mentioned he's a little over 2,000 years old, because that's how much he's lived and aged and been conscious about it. However, when he's in the confession dial, it states he's been trapped in that loop for about 4.5 Billion years.

But, due to him 'resetting' himself after a couple days, he did not age 4.5 Billion years, he only aged a couple of days, making him still only a little over 2,000. The 4.5 Billion does not count toward his age.

But it does count toward his existence. He may not have aged, but he still existed all of those 4.5 Billion years. Just because he reset himself in the teleporter doesn't mean he simply ceased to exist the previous days or years, as evident by the billions of skulls in the lake, those are still his, he still existed.

The Doctor's Existence is billions and billions of years old, but he's only aged 2,000 of those years.