Why do we continue paying the installment of a trade in iPhone?

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Because you still owe payments on the old phone.

If you financed the phone, you need to complete the payments as you owe the entire value of the phone wether you have it or not.

If you Used the trade in option, this is entirely separate to the financing of the phone. the phone would have been valued at some price, and you should have been given a value, and had to accept it. However this in no way ends your prior financing commitment for the previous phone. That's not how the Trade In works.

The only option that lets you get a phone for monthly installments and then upgrade to a new phone every year is the iPhone Upgrade Program. but in that case, there is no trade in value applied to the new iPhone. You simply send the old phone in, and get a new one and start the payment plan over again for the new iPhone. The previous payment plan is then cancelled.

The iPhone Upgrade Program, the Apple Card monthly installments and the trade in are all separate processes.

Sounds like you were confused about how the installment plan you had works.