Update 2:

Maybe this policy is different among stores. Some people said that Apple refused to apply their trade-in value to the original purchase. When I picked my iPad mini 6 at the Apple store (in the US), I asked Apple's Specialist whether if I could trade in later, and they said yes. So when I went there yesterday (13 days later), they processed it right away without any problem.

Therefore, you should ask Apple's Specialists first to confirm whether if they allow you to trade in your old device later.

Update 1:

If you choose the mail-in option for online trade-in, the Apple store will refuse to process your trade-in at stores.

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TLDR:

Trade-in your old devices at the Apple Store within 14 days of a new purchase. Never trade-in online. Ask Apple’s specialist to confirm this trade-in policy just in case they change it later.

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Original post:

When you purchase a new device at Apple Store or on the Apple website, you don't have to trade in your old device to get the credit right away. You can do that within 14 days when you are satisfied with your new device. That's what Apple employee told me.

When you bring your old device to the Apple Store to trade in later, just show the Apple Specialist the invoice along with the serial number of the new device that you bought, so they could apply the credit to the device in that order. Moreover, they will ask you to give them your credit card/debit card so they can send the credit to that card. It takes 3 days for the credit to be applied to your card.

I just finished traded in my old iPhone after 14 days since the day I have bought my new iPad mini, and they accepted that without any problem. So I think this info is useful for people who want to try a new device before they decide whether if they should sell/trade in their old device.

If you decide to trade in your device to Apple, please do it in person at the Apple Store. The process is quick and easy, and you get the maximum value of the trade-in right away. Never apply for the trade-in on the Apple website because Apple will assign a third-party company to serve you. They will send you a box so you can send your old device to them. It is a sketchy company. You have to wait in 2 weeks then they will tell you that your device has a problem, so they offer you a very bad quote with a lower value. When you ask them to send your device back to you, you will receive a “broken” device with problems that you have never seen.

Edited: Fix typos.