Analysts were quick to see the benefits for Apple in the company’s new iPhone Upgrade Program, the one announcement that took everybody by surprise at Apple’s AAPL Sept. 9 iPhone event.

What they couldn’t foresee was whether Apple’s customers would see the benefits to the buyer. Piper Jaffray’s Gene Munster, for example, predicted that 15% of new iPhone customers would opt for what is, in effect, a 24-month lease.

He was way off.

In a note to clients issued late Monday, Munster reported that of 188 iPhone 6S buyers surveyed in mid-November, 70 people (37%) chose the new program. By the end of the quarter, Munster believes, the actual rate could turn out to be as high as 50%

The deal is basically a leasing program with benefits.

For 24 relatively low monthly payments—anywhere from $32.41 to $44.91—customers get AppleCare+ phone support/damage insurance (a $11/month value) and the option to trade up to an iPhone 7 (or whatever it’s called) a year from now.

 

AT&T ATT , Verizon VZ and T-Mobile TMUS have started offering similar deals on somewhat sweeter terms, but Munster believes many customers will prefer to deal with Apple than with a carrier. “In that regard,” he writes, “we believe Apple has the upper hand.”

As we wrote in September, the upgrade program is a good deal for customers and an even better deal for Apple.

  • It gets to sell more high-margin AppleCare+ contracts
  • It locks customers into the iPhone indefinitely
  • It halves, in theory, the iPhone upgrade cycle (to 12 months from 24)
  • It builds an inventory of used phones that can be refurbished and resold
  • It takes control of, and legitimizes, the grey market for second-hand iPhones
  • It unbundles hardware costs from carrier costs
  • It leaves cell service complaints clearly in the carriers’ hands
  • It could raise, according to RBC Capital, Apple’s iPhone profit margin from 50% to 55%.

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No wonder Apple is pushing the plan hard for the holidays in its retail stores, on its website and, most recently, in unsolicited e-mails.

Munster predicts that 75% of Apple’s iPhone customers will eventually move to an annual upgrade, lifting Apple’s U.S. iPhone unit sales 10% over the next three years.

Follow Philip Elmer-DeWitt on Twitter at @philiped. Read his Apple AAPL coverage at fortune.com/ped or subscribe via his RSS feed.

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