Hi Comsonic,
welcome to the Apple (user-to-user) Community.
Re: Trade in with phone value"
Seems you could get an estimate of the trade-in value online to help you calculate:
Apple Trade In - Apple
Also, the Shopping Help - Apple webpage has lots of info., on finding answers.
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Re: "will I have to pay both phones for a little bit while transition to my new contract ..."
We are all Apple users, like yourself, in the community ... we can not speak for Apple ... (and how your particular transaction / transition / will work out would need more finer financial details than we can discuss here.)
Eg: You may need to check out the actual transaction with the online help available during an online purchase,
or you could phone Apple in your country or region:
See a list of Apple phone numbers around the world. Contact Apple for support and service - Apple Support
If your country is not listed: Apple Assistance: Choose your country or region - Official Apple Support
All the best :-)