It is unclear where the rumors stemmed from. However, given that Apple's most recent iPhone —the iPhone 4S — ranges in price from $199 to $399with a wireless contract, the steep increase in price seems highly unlikely.
Still, the cost of the next iPhone could be $800 or more if the buyer doesn't commit to a wireless contract.
The current price for an unlocked iPhone 4S, or an iPhone bought at retail price without a contract, is $649 for the 16GB iPhone, and $849 for the 64GB version.
In that context, the new iPhone pricing at $800 is reasonable based on Apple's current prices.
Earlier this month rumors spread that Apple would be releasing a new iPhone on Sept. 12 with a release date of Sept 21. And while Apple won't confirm rumors about possible release dates, the company is known to release its iPhones in the fall.
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