Despite the recent $20-a-year price increase, Amazon's (NASDAQ:AMZN) Prime service apparently continues to sign up new members. 

The program, which offers free two-day shipping on millions of items, as well as other benefits including free video and music services, may have as many as 50 million members worldwide, according to a recent Re/Code article that references a research note from RBC Capital. Though Amazon never releases specific membership totals for the service, the company has acknowledged it has "tens of millions" of people paying for the Prime service.  

RBC Capital Analyst Mark Mahaney now believes the company has between 30 million and 40 million Prime members in the U.S. and between 40 million and 50 million in total worldwide, Re/Code reported. The estimate is based on an RBC survey of more than 4,000 Amazon customers.

If the numbers are accurate, it shows that despite the March increase of Prime's price from $79 to $99, Amazon is not only keeping members, it's adding them. That's especially important when you consider that Prime members spend a lot more on Amazon than their non-Prime counterparts.

What does a Prime member do for Amazon?
Amazon Prime members spend an average of $1,340 per year, a little over double the $650 that non-members spend, according to a survey conducted by Consumer Intelligence Research Partners in November 2013. That's in line with RBC's estimate that Prime customers spend 2.3 times more per year.

Better yet for Amazon, CIRP reports that Prime members buy from the company more often -- 22.5 times per year -- while regular customers do so only 13.9 times per year. That 22.5 number is especially important because it's actually below where Prime members could be "making money" on shipping since the site does have its lowest rate approaching $3.98 for non-Prime members.

Admittedly it's a rough calculation, because shipping fees do vary, but Slate's Amazon Prime Calculator shows that it takes 25 eligible purchases to push the cost of delivery -- when averaged out over the $99 price of Prime -- below $3.98 per shipment.

At 22.5 deliveries, and in the perfect-case scenario, Amazon is essentially making money as the company -- at $3.98 a delivery -- covers the $89.77 in shipping charges it would collect from a non-Prime member. That leaves a little over $10 per customer -- or $500 million -- to pay for Prime's video and music services, which are free for members.

That likely does not cover the full cost of the services, which Amazon does not disclose, but it lessens the impact of the Prime perks on the bottom line. It's also possible that shipments per Prime member will go down as more digital content is delivered.

Piper Jaffray estimates annual churn for Prime will be 5% ; CIRP estimates it will be 6%, according to fellow Fool Brendan Matthews, who breaks down the impact of Prime members on Amazon in a unique way.

In some ways, Prime membership is a lot like joining a gym, where the value to customers is in what they should or could do, not what they actually do.

Prime members are good customers
If a Prime member wants to game the system, he can by placing lots of one-item orders for cheaper merchandise. Free shipping could easily be taken advantage of, but Prime members aren't doing that.

Most companies offering unlimited anything would end up with the equivalent of the all-you-eat buffet, where customers avoid bread in order to load up on shrimp and prime rib. In Amazon's case, people are essentially eating reasonable portions of a little of everything and stopping when full.

Having Prime makes customers use Amazon more often and spend more per shipment. This aids Amazon's efficiency while keeping shipping costs down.

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An Amazon fulfillment center. Source: Amazon. 

Keeping Prime customers happy is key
An extra $690 a year per customer adds up pretty quickly. (That's the difference between what Prime and non-Prime members spend on Amazon.com, according to that Consumer Intelligence Research Partners survey). At that amount, every million Prime members would mean an extra $690 million in sales per year, so if the number is really 50 million, then the company is reaping nearly $35 billion in added sales due to the loyalty program.

There's also some added benefit as more sales mean more page views (Amazon does sell ads), more loyal customers to sell new devices to, and more people to pitch new services to. Whether it's groceries, Fire TV, or even drone delivery, Prime gives Amazon a willing audience to grow its brand to.

Given Amazon's razor-thin margins and lack of consistent profits, Prime members become even more valuable. They buy more and have what they do buy sent in fewer shipments. They also think of Amazon first and make competing with the online leader a more daunting challenge for anyone else.

Daniel Kline has no position in any stocks mentioned. He is a Prime member who does not order enough for it to be a worth it. The Motley Fool recommends Amazon.com. The Motley Fool owns shares of Amazon.com. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.