over in the "AT&T Says Samsung Galaxy S4 Mini to Street May 23" discussion:
Next Program with Samsung S4 mini
The next program payments are 20 month term and 26 month term. On the 20 month term agreement you can trade-in the phone on the 12th month and get another device on the next program. The 26 month term you can do the same trade-in on the 18th month.