A couple weeks ago, analysts from Morgan Stanley released a report suggesting Amazon's (AMZN 0.16%) Prime service may be reaching saturation in the United States. Forty percent of U.S. households had a Prime subscription as of the fourth quarter last year, according to the analysts' survey. While impressive, that's the same number they found in the fourth quarter of 2016.

But rest assured, Amazon investors: Amazon Prime is still growing rapidly. In fact, the king of online retail just announced it added more Prime subscribers in 2017 than any other year. Of course, it got a lot of help from expanding to new international markets like India, China, Mexico, and Singapore in the last couple years. Still, there's plenty of room for Amazon to keep growing Prime.

There are three major factors pushing Prime: the growth of Amazon's branded device sales, increased engagement with digital media benefits, and the continued expansion to new international markets. And Amazon is always looking for ways to improve Prime to make it attractive to everyone with a wallet.

One of Amazon's Prime Air airplanes.

Image source: Amazon.

"Alexa, I need more dog food"

Amazon's Fire TV Stick and Echo Dot were "the best-selling products purchased by U.S. Prime members from any manufacturer in any category across all of Amazon," according to Amazon's press release.

Amazon had a surprise hit with the Echo speaker, and it's capitalized extremely well on that success by incorporating the core technology -- digital assistant Alexa -- into nearly all of its devices. The assistant is particularly great at making it almost too convenient to shop on Amazon versus its competitors. Amazon devices also prominently display the digital media offerings available to Prime members.

While the press release notes these devices are purchased by customers that already subscribe to Prime, it's worth noting that they make the service that much stickier. Amazon devices lose a lot of their functionality without a Prime subscription, so there could be a feeling of sunk costs for some consumers. That helps reduce subscriber churn.

There are also likely a good number of Amazon device sales to non-members. These can be a way for Amazon to onboard them by displaying what customers can unlock with a Prime subscription. In fact, Amazon introduced the ability to sign up for Prime through Alexa last summer and offered discounts to customers for doing so.

"Alexa, play The Grand Tour"

Perhaps one of the reasons Prime subscribers are buying more devices is to watch and listen to more of the digital content available through a Prime subscription. Amazon heavily increased its content spending this past year, and it produced a compelling slate of new original series and movies. It also continued to offer a small music streaming service with a slightly older catalog than mainstream services, as well as a selection of free e-books.

Amazon says "Prime members around the world used Prime digital benefits this year more than ever before." So, it appears its investments are paying off.

Prime video has turned out to be a major loss leader for Amazon. And with the step up in content spending this year, that probably isn't going to change anytime soon despite the record subscriber additions. But the engagement with Prime's digital benefits indicates the spending is attracting new subscribers and keeping old ones.

Continued improvements in the Prime video catalog and Prime's other digital benefits should help attract still more consumers.

"Alexa, necesito mas comida para perros"

Amazon expanded Prime to four new markets in 2017: Mexico, the Netherlands, Luxembourg, and Singapore. While those countries likely contributed a few new Prime subscribers, the biggest growth more likely came from India and China, which Amazon expanded to in 2016. India, in fact, is Prime's fastest-growing market.

Still, Prime is available in just 16 countries. Meanwhile, Prime Instant Video -- a video-only version of Prime -- is available in over 200 countries. The video service is a clever way for Amazon to establish a relationship with more customers in new markets before it enters those markets with its retail operations in earnest.

Investors should expect Amazon to continue expanding Prime internationally. There are tons of opportunities in both emerging and developed markets that Amazon has yet to take advantage of, and it's still only getting started in India and China -- two of the biggest e-commerce markets in the world.

"Alexa, refill my prescription"

Amazon still has more opportunities to attract customers to Prime.

Following the acquisition of Whole Foods, Amazon said it would make Prime the loyalty program for the grocery store chain. While there's a lot of overlap between Whole Foods shoppers and consumers already subscribed to Prime, it's one more benefit that may onboard a few new customers while giving existing subscribers yet another reason to subscribe again next year. Amazon could also link Prime to a grocery delivery service, leveraging its Whole Foods acquisition.

Amazon is also reportedly interested in getting into the pharmacy business. It could offer discounts to Prime subscribers, or simply rely on its free same-day and next-day shipping it offers Prime members in certain cities to drive more customers to its online pharmacy and fill their prescriptions.

With every new vertical Amazon explores, it's an opportunity for it to make Prime even more appealing to more consumers. Investors shouldn't expect Amazon to stop until there's absolutely no more room to grow. And there's certainly still room to grow in 2018.