Mr. Moffett explained why: “This is the first iPhone cycle when what’s known in the industry as E.I.P. — or equipment installation plan — is really popular among the big carriers. They’re giving a lot of discounts. And you may be able to get a better deal that way right now, if you’re willing to look for one. Unfortunately, many Americans are allergic to math. And you may have to do the numbers yourself to find out which plan is better for you.”

I started buying an iPhone 6 on AT&T’s website the way I always have, with a standard two-year service contract. But this time, I was surprised to discover that if I continued down that road, AT&T would penalize me in two ways.

This part may be tedious if you’re not at least a little nerdy, but please bear with me:

First, AT&T said it would charge me a $40 “upgrade fee.” And then, as I went further, a warning popped up. It said that while I could pay $199, I would no longer be “eligible for the Mobile Share Value monthly discounts” of $15 or $25 a month. In my case, it’s $25 a month. That’s because I use a lot of data: I’m part of a family-sharing plan that gives us 10 gigabytes of data a month.

If I got a phone for $199, plus $40 for an upgrade fee, I’d “lose” — that is, have to pay — $25 a month for my service plan for two years, or $600. Add all of that up, and it comes to $839. If you use less data, you’d presumably “lose” $15 a month for two years, or $360. Using the same calculations, you’d end up paying $599.

And there’s more. Because even the smaller and cheaper of the two main versions of the iPhone 6 dwarfs the iPhone 5 that I carry in my pocket, the protective case I’ve got now won’t fit on a new phone. And I won’t risk dropping such a precious gadget without a case. With a corporate discount, the cheapest replacement case I was able to find on the AT&T store goes for $16. Ouch. Tack that onto the final price.

That’s for a basic iPhone 6. Apple, you’ll recall, says the phone costs “from $199.” Hmm.

I found an excellent article on ZDNet by Ed Bott, who did this sort of calculation for a variety of plans and carriers. He concluded this way: “You know what? You can’t get an iPhone 6 for $199. And anyone who tries to tell you otherwise needs to go back to smartphone school.” I went back to smartphone school, with the help of Mr. Moffett.

I found that if I bought the iPhone from AT&T and qualified as a good credit risk, I would receive a 0 percent loan for the full cost of the phone and could pay it off over 24 months at $27.05 a month, which comes to a little more than $649. Let’s round that off at $650. There’s no $40 upgrade fee. And there’s no $199 down payment. (I would have to pay sales tax on the $649 cost of the phone.) For me, I concluded, it would be cheaper to buy the phone from AT&T on the installment plan. If I used less data, it would be cheaper to buy the phone from AT&T through a service contract. And, of course, there are different deals on different carriers.