A scene from “The Mandalorian,” an original Star Wars TV series that will stream on Disney+.Source: DisneyDisney said on Thursday evening it’s forecasting Disney+ will have 230 million to 260 million subscribers by 2024. It shows the rapid growth of Disney+ and that Disney is emerging as one of the early winners of the streaming wars.Disney shares were up more than 8% in the premarket.When Disney+ launched 13 months ago, Disney said it expected the platform to reach 60 million to 90 million subscriptions by 2024. Then the streaming platform quickly took off. As of Thursday evening, it had already closed in on the high-end of that projection, with 86.8 million Disney+ subscribers.It’s an impressive goal, especially since competition in the space has only increased. Apple TV+, Netflix, AT&T’s HBO Max, Comcast’s Peacock, ViacomCBS’s Paramount+ and AMC Networks’ AMC Plus are all competing for eyeballs. Discovery CEO David Zaslav, who recently announced Discovery’s premium service Discovery+, recently told CNBC the winners and losers of the streaming wars will emerge in the next 12 to 24 months.Here’s a quick rundown of Disney+’s rapid growth: Ten million people signed up within the first day, with a total of 26.5 million subscribers in its first operating quarter. Disney+ jumped from 33.5 million subscribers in its second quarter to 57.5 million by its third quarter. By the fourth quarter, the company said it surpassed 73.7 million subscribers.Some of those subscribers arrived at the service through bundles or one-time promotions, like a partnership with Verizon that offered one year of Disney+ to customers, though Disney doesn’t break out those numbers.By comparison, Netflix reported 195.15 million subscribers in the third quarter. Earlier this week, AT&T CEO John Stankey said there are now 12.6 million HBO Max subscribers.Disney has invested heavily into its direct-to-consumer business, as the Covid-19 pandemic continues to keep millions of people at home and in need of entertainment. The company will continue to push into original content, with new shows and movies likely being able to bring in even more subscribers.CEO Bob Chapek said at Disney’s investor day Thursday of the roughly 100 projects that were announced, about 80% will go directly to Disney+. Disney will allow users to opt-in for more mature content, which will enable older audiences to watch titles like “Atlanta” and “Modern Family.” That could also helps attract more subscribers.As it expands content, Disney said it plans to increase the cost of the service to $7.99, up $1.Disney added that it expects its family of streaming services, which includes Disney+, Hulu and ESPN+, to hit 300 million to 350 million total subscriptions by fiscal 2024.Subscribe to CNBC on YouTube.