Didn’t they say somewhere the contract expired?
Well, several things. First off, Apple has never bought a Qualcomm license. If they did, they'd have to pay much more for the patents. Instead, they cleverly let the various factories use their own licenses to pay only on the price that they charge Apple for a boxed iPhone. E.g. $240 for a $700 retail phone.
That's why the royalties mentioned in articles were at one time only about 3.25% of $240 = ~$7.80 per phone. Apple was not paying royalties based on the huge extra profit that they take from their own customers.
As for the rebate contract, it was in return for Apple exclusively using Qualcomm chips. Apple didn't have to sign of course, but their greed overrode their common sense. No different than the way that GTAT agreed to exclusivity with Apple and later regretted it. But regret is not a legal reason to stop paying, and it's not a reason to claim that they "couldn't buy from other modem makers".
Apple stopped honoring it after Qualcomm withheld rebates because they said Apple broke some of the contract provisions.
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The real reason why Apple had no other modem choice was because most standalone modem makers went out of business when phone makers everywhere started making / using INTEGRATED CPU + MODEM chips. Mediatek, Samsung, Huawei, everyone used an integrated processor set.
Apple is nearly alone using a separate CPU and modem. So it wasn't until Intel got interested, that Apple had a choice (other than say, a standalone Mediatek). And it's a good bet that Apple will leave Intel behind as well, once they hire away enough people to make their own integrated device.
Honestly, it's really hard to get worked up about two highly profitable companies each wanting to make more profit. But in the end, Apple stashing away more billions does nothing for us. OTOH, Qualcomm making more gives the whole world faster and better data technology.