No, you wouldn’t. It’s paid on first registration, so the £180 rate would apply from that point onwards, even if 1 day after registration. The original owner would only be refunded based on the £180 rate, I believe.
...and in your example, if it's original cost was over £40k, you'd only pay the enhanced rate for 5 years 9 months, not the full 6 years. (The higher rate is valid for 5 years after the first tax renewal).
