If I don't have a contract can I still update my iPhone 5s to the iphone 6?

I have T-mobile if that matters

Yeah, Tmobile does matter. That's their question. Why? With that 'plan' where you make payments on the phone like you have they allow you to trade it back in after so many months. But they will only give you up to 50% of what you owe on it to pay it off. If they do pay it off, then you just start fresh and pony up the coins to buy the 6. Best luck.

Yes you can… If you buy a new iPhone 6.
You're off contract! Of course you can't

Yup. You have to pay more money