New car sales tax calculation

Going to buy (finance) a new car at $55,000 OTD.
Trade-in a lease with 6 months left to maturity.
Allowrance: $37,000 and Buyout: $38,000, roll in $1K negative equity

When calculate the sales tax, the dealer was using 55K x 6.25% instead of (55K-37K)x6.25%, is the dealer correct?

Did you pay sales tax for the full amount of the car when you leased it?

Why would they deduct $37k now? It’s a leased car.

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