This isn't actually a metamagic feat, because it doesn't actually do anything to spells, so I think you'll have to drop the Metamagic tag. Also, time wouldn't fall under D&D multiplication, since it's a real value and not an abstraction. Not really an issue, and the feat itself seems just fine. I was originally going to edit it into a standalone feat that just can't be applied to extended spells, but I couldn't figure out a way to do that that doesn't read like ass. So that awkward little Special line worked its way in.
Persistent Spell
You have learned how to greatly extend the durations of your spells.
Prerequisites: Extend Spell
Benefits: You may apply Extend Spell multiple times to the same spell. Instead of doubling the spell's duration for each additional application of Extend Spell, increase the duration by whatever the spell's duration would have been prior to any metamagic feats.
Special: Persistent Spell is considered a metamagic feat for the purposes of selecting bonus feats and meeting prerequisites.