Eurythmics Rocker -- Teen Daughter Gets Big Break ... Sweet Dreams Are Made Of This

The 14-year-old daughter of Eurythmics guitarist David Stewart is ready to break into the family biz, but she's not exactly breaking the bank ... TMZ has learned.

Kaya Stewart inked a deal with Warner Bros last month -- and even though she's 80s rock royalty ... the contract calls for a relatively modest $100,000 advance. She has 6 months to complete her first album.

She’s got the voice to pull it off -- Kaya's performed Eurythmics classics with her dad on many occasions.

According to the minor's contract -- obtained by TMZ -- Kaya will get another $50,000 once the album's complete ... and the dollar figures increase quite a bit if her career catches fire.

Kaya's deal is for 5 records ... and she'll take bank up to $550,000 for the last one ... before royalties.