At the start of this US Open, Jessica Pegula did something that millions of New Yorkers do every day.

A video posted on her Instagram account shows her riding the subway – although unlike most passengers, here she is lugging tennis bags around with her and preparing for her eighth major match in Queens.

“For me, it’s normal,” said Pegula, the current world No. 5 and daughter of billionaires Kim and Terry. “And people say, ‘Oh my God, I can’t believe you did that.’ And I ask, why? I like taking the train. I like taking the subway.”

“It’s kind of weird when people assume I fly everywhere on a private plane or that I’ve had a chauffeur driving me around since I was five,” she added. “I’m like, what? Or I have a butler… it doesn’t work like that,” she said.

Pegula, who spoke exclusively to Mail Sport after her second-round win over fellow American Sofia Kenin, is an affable personality who – like her WTA colleagues – has been training for a professional career since she was a child.

Jessica Pegula’s family is worth billions, but she thinks her fans are sometimes wrong about her

However, it is easy to see where these assumptions come from.

According to Bloomberg, Pegula’s father, Terry, sold most of his natural gas company for a whopping $4.7 billion in 2010, and four years later the family purchased the NFL’s Buffalo Bills.

Last summer, a headline following her exit from Wimbledon even blamed her sixth consecutive Grand Slam quarterfinal defeat on a lack of “dynamism” that “billions of her family’s money couldn’t buy.”

However, the 30-year-old stresses that her family only acquired their enormous wealth when she was a teenager and that people sometimes have “a wrong image of her in their heads”.

“People jump to conclusions that are completely overblown. I grew up pretty normal, and a lot of this (their family becoming billionaires) didn’t happen until I was older and playing. Since I was six or seven, my goal was to be number one in the world. So that was before a lot of these other things happened. I mean, before that, I was a normal kid growing up in Pittsburgh, Pennsylvania, taking after-school classes. So I think that’s just the kind of difference that the casual fan might not understand as well.

“It’s usually some people on the internet who, I don’t know, probably have nothing better to do,” she added of the barbs involving her family’s wealth. “But I would say, I think everyone on tour knows me really well and obviously knows it’s not easy. So I don’t think there’s a lack of respect, at least from the people I work with.”

Pegula (left) is pictured with her family after her parents Terry (center) and Kim (right) bought the Buffalo Bills in 2014

Pegula reached the third round after defeating American Sofia Kenin on Thursday

And that should be the case, as Pegula has had an impressive career, establishing herself as the second-highest-ranked American behind Coco Gauff.

She has made it to the last eight of every Grand Slam tournament – ​​but never beyond – as doubts naturally arose about her ability to break through.

Pegula led 4-1 in the final set of her Wimbledon quarter-final against Marketa Vondrousova last year and had one break point before ultimately losing the match. She eventually changed coaches in February after being knocked out in the round of 16 by Queens last year.

Speaking about the decision to part ways with former coach David Witt, she previously said she was approaching the “end of her career phase.” Since making the change, her year has been up and down, with second-round exits at this year’s Australian Open and Wimbledon before reaching the final in Cincinnati earlier this month.

Nevertheless, she seemed optimistic in her speech at the Billie Jean King National Tennis Center – and is inspired by a male player seven years older than her.

“To see someone like Novak (Djokovic) play, who is obviously still one of the best players in tennis… at such an old age, definitely. I think you see people still perform well at an older age and that definitely helps.

“Obviously, I’m not going to go backwards now that I’m 30,” she continued. “I think I’m just facing a new life with new challenges and maturity and I just want to know that I’ve given myself time to maybe try some different things.”

Pegula has also found motivation at the other end of the age spectrum.

She has spent a lot of time playing doubles with and getting to know the 20-year-old Gauff and was delighted when she won her first Grand Slam title in Queens last summer.

Along with Gauff, the soon-to-be-retired Danielle Collins, Emma Navarro and Madison Keys, Pegula is one of five Americans currently ranked in the top 20. But she obviously wants to be the next to make her big splash.

“I really enjoyed watching her win that last year,” she said of Gauff. “Of course I would love to win one too. But it definitely helps when you play and train with someone and then see how well they do. It’s definitely motivating.”

Pegula and Coco Gauff met as doubles partners, and the former said she was happy that her fellow American won the US Open last year.

Pegula cited 37-year-old Novak Djokovic as her inspiration for starting a new phase of her career

“And I felt like a lot of American girls are doing that right now. I mean, there are a lot of us, and we all see how well everyone else is doing, and when you see that, you feel like you can do the same thing. So that’s always motivating and inspiring to see.

Pegula has defeated two American players in this tournament, Kenin and Shelby Rogers, and will face Spaniard Jessica Bouzas Maneiro in the third round on Saturday.

Of course, the further she gets in the tournament, the more the horrors of her previous quarterfinal losses will linger in her mind, but for now she is living in the present – having already achieved her best Grand Slam result this season.

“I have to trust that I can do it if I continue to put myself in these situations,” she said.

“…Of course I would like to get over the hill, but at the same time I have to get there first.”