Despite a straightforward fourth-round win over Diana Shnaider, something had irritated Jessica Pegula.

“The most annoying thing is that people think I have a butler,” the 30-year-old American said on Monday.

“That I get chauffeured around. That I have a private limo. That I fly on a private jet everywhere.

“I am definitely not like that.”

The misconceptions about her lifestyle come from her family’s wealth. According to Forbes magazine, her father Terry, an oil and gas tycoon, is worth $7.7bn (£5.9bn), making him the 371st richest person in the world.

She is not the only billionaire’s daughter in the last four of the US Open on Thursday.

On the other side of the draw is Emma Navarro. Her father Ben owns a credit card empire and, according to Forbes, is worth $1.5bn ( £1.1bn).

They are numbers that put even the $3.6m (£2.7m) prize money for the Flushing Meadows champion – the biggest cash prize in tennis – in the shade.

But there is some way to go before Pegula and Navarro can book in for a box-office, big-money, all-American battle for the title.

Two-time Australian Open champion Aryna Sabalenka, the highest seed remaining in the draw, has shown strong form en route to her meeting with Navarro, while outsider Karolina Muchova has a happy habit of claiming big scalps as she prepares to face Pegula.

BBC Sport looks at the form and the stories of the four semi-finalists.