Source: Apple.

In just over three months, Apple (AAPL -0.26%) has created the second-largest paid music service in the world. Apple Music's 6.5 million paid subscribers are short of only market leader Spotify, which recently reported 20 million paid subscribers. Apple CEO Tim Cook added that there are 8.5 million more users still trialing the service. Spotify, comparatively, has 55 million users on its ad-supported free service.

Apple Music's early numbers are certainly a great start. Let's look at how it got there and what investors can expect going forward as Apple tries to overcome the seven-year head start it gave Spotify.

She works hard for the money
In August, Apple announced that 11 million users were trialing Apple Music. Just about all of those trials have expired now, so Apple is converting people that sign up for the trial at around a 59% clip. That's pretty phenomenal, considering the Apple Music app has gotten torched by reviewers, claiming it has a clunky interface and can be confusing.

Spotify has historically converted 25% of free users into paid subscribers, but its most recent update showed an improvement to 26.7%. Those numbers may be boosted by Spotify's recent promotion offering three months for $1. Since those listeners are technically paying, Spotify is probably lumping them in with subscribers paying $10 per month.

Additionally, Apple is signing up free trial users at a relatively strong rate. Since it announced its 11 million free trial signups in August, the company has added 8.5 million new trial users -- about 3.5 million per month. That's slightly faster than the 3 million net new listeners Spotify added per month in first half of 2015.

If Apple can keep up its trial and conversion rates, it could surpass Spotify's paid subscriber base within a year. Apple Music has yet to expand to Android, and its advertising is mostly branding instead of product focused. There's still room for Apple Music to improve its numbers.

Churn, baby, churn
A large portion of those 6.5 million subscribers will likely cancel their subscriptions in November after realizing they forgot to cancel before their trials ended. Music industry analyst Mark Mulligan predicts about 1.5 million subscribers will cancel their subscriptions after paying for one month, leaving Apple Music treading water through the end of the year. He believes Apple could have as many as 10 million cumulative subscribers by year's end, but only 6 million active.

Six million active subscribers would put Apple's conversion rate much closer to Spotify's, but Apple Music doesn't benefit from placing ads in any of its content. Non-subscribers can still use Apple Music Radio (which does have ads) and listen to Beats 1 (which doesn't).

There are two solutions to this problem. Apple could do a better job of funneling potential users into Apple Music through better promotions and expanding to other computing platforms. Or it could improve the user experience in the app, cutting out extraneous parts and making it easier to navigate. Apple should do both. It would have a positive impact on total trials, conversion rate, and churn rate.

Some churn is to be expected from people taking a free trial and then failing to cancel in time, but Apple needs to keep it under control.

Sweet streams (are made of this)
While Apple has attracted 15 million listeners to Apple Music, Spotify says it continues to add more subscribers. Music Business Worldwide reports that Spotify's users have accelerated since Apple Music's release, and it's expected to release new metrics touting 100 million total listeners.

Many other streaming services continue to grow as well. That means these subscribers are probably converting from digital downloads to streaming. The integration of Apple Music with iOS brings all the functionality of a locally hosted library of songs to a streaming service, which may be a strong selling point for heavy iTunes downloaders. As a result, Apple is cannibalizing itself.

It was a necessary step, however, as music streaming has been cutting into digital downloads for some time now. iTunes music sales declined 13% last year. Spotify and the cavalcade of smaller music services have made a significant dent in iTunes, but Apple Music is off to a strong start to offset the competition.