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Hello, I am Keith, one of the experts on Just Answer, and pleased to be able to help you with your question.
You are correct in your surmise for the sale of your old vehicle.
For the new vehicle the ball game has changed dramatically and, depending upon the car's CO2 emmission and when it was acquired, you can even get First Year Allowances. The conditions are complex and you can find them here:
I do hope that you have found my reply of assistance.