We are fast approaching the timeframe for Apple to launch a new iPhone model, and speculation is growing as to what date we can expect to see the iPhone 5S rolled out. The latest prediction? The iPhone 5S will be unveiled on September 10 and be available to buy on September 20.Tim Cook made it clear earlier this year that we wouldn’t be seeing a new Apple device released until late September at the earliest. September 20 certainly falls into “late September,” but the reason that date is predicted has more to do with iOS than the iPhone hardware.When iOS 6 was first introduced last June, the mobile OS was released exactly 100 days later. Dave Smith of the International Business Times expects the same to be true of iOS 7, which was introduced during WWDC this year. 100 days added to that would be September 18. That’s a Wednesday, and iPhones are traditionally made available on a Friday, which is why September 20 is the key date. Also note that the iPhone 5 launched on September 21 last year, two days after iOS 6 was released.As for when Apple will unveil the iPhone 5S on stage and detail why it’s great, that event is expected 10 days earlier on September 10. At the same time, Apple is also expected to introduce a new, cheaper iPhone that will sell at a much lower price point, but loses a number of features and uses a plastic casing.That cheaper model won’t be going on sale at the same time as the iPhone 5S, though. Apple intends to wait a few weeks to launch, maybe even into November, in order to avoid any consumer confusion.