Americans continue to warm up to paying for streaming music.

The latest evidence surfaced Tuesday when Sirius XM Radio reported that it added 411,484 paid subscribers in the fourth quarter — helping it beat Wall Street revenue forecasts for the period.

The strong fourth quarter for signing up paying subscribers — as opposed to those who get a free trial with their new car — brought 2013 self-paid subscriber sign-ups to 1.5 million for the year.

Sirius projected it will add another 1.25 million customers in 2014 willing to fork over at least $9.99 per month.

The satellite-radio company, currently considering a takeover bid from majority shareholder Liberty Media, reported a 12 percent increase in fourth-quarter revenue to $1 billion.

Profits of $65.2 million, or 1 cent a share, fell short of expectations. As a result, Sirius shares fell nearly 1 percent, to $3.52, on Tuesday.

“It seems there’s this huge battle for the consumers’ wallets in the $10 range,” said Ken Doctor, an associate analyst with Outsell.

Doctor noted that Sirius has a serious lead over rivals, but Pandora and Spotify are out there fighting back.

Pandora recently started signing up deals with automakers. Its $36-a-year premium Pandora One service has not bowled over the public yet — but investors may get an update when Pandora reports results Wednesday.

Spotify, which offers its own $10-a-month service, made a push recently by offering a free tier — and some 4 million tried it out, sources said.

Separately, SoundExchange, which collects fees from digital radio players, recorded a 28 percent rise in revenue in 2013, to $590.4 million. That reflects both an escalation in royalty fees paid by the likes of Sirius, which cuts it a percentage of revenue, and an increase in music streamed.

SoundExchange is suing Sirius for $100 million in nonpayment of fees for music recorded before 1972.