The Obama daughters have gotten closer as they've gotten older, their dad says

Very few kids grow up in the White House, in front of the whole country (and under Secret Service supervision). But Malia and Sasha Obama got through it together.

Now nearly four years after their dad, Barack Obama, left office, both 22-year-old Malia and Sasha, 19, are in college and have been spending much of the past year with their parents, social distancing amid the pandemic and taking classes remotely.

"Malia and Sasha have been with us almost continuously since March, with just a few breaks," Obama, 59, tells PEOPLE in this week's cover story looking back at his presidency and new memoir, A Promised Land. (The family shared with PEOPLE a few never-before-seen photos from their post-White House life, including one of the four of them in July 2019, when Sasha graduated from high school.)

Life in quarantine this year has had its many ups ... and it downs, Obama says.

"Like a lot of families who are lucky enough not to have to worry about losing a job, or a family member getting sick, there are times where it's felt claustrophobic, I'm sure, for them," he says of his girls.

"But for Michelle and me as parents, to have this bonus time where your kids are having dinner with you every night and we're playing games and watching movies together — there's been a lot of joy to that," he continues.

As his daughters have grown older, they've also grown closer.

"I think part of what's been also wonderful is seeing Malia and Sasha become such great friends," their dad says. "They've got a three-year gap between them, and when one is 16 and the other one's 13, there's still that sister competition," he says, a little wryly. "‘Did you grab my halter top? Where is it? Why haven't you returned it? Why are you doing this, why are you doing that?’ "

But such squabbles are a thing of the past. 

• For more from PEOPLE's interview with former President Barack Obama, including details of the former first family's life together in quarantine this year, subscribe now or pick up this week's issue, on newsstands Wednesday.

Barack Obama People Cover
Barack Obama PEOPLE cover
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"Now they're both old enough, where they just enjoy each other's company," Obama says, "and to be together as a family and see how they've become these marvelous young women — there's been no greater joy than that."

Malia is in her senior year at Harvard University, while Sasha is a sophomore at the University of Michigan. 

Earlier this year, former First Lady Michelle Obama said that the family had gone through stages of their increased time together, which was nice but not always easy.

"We've kind of had phases of COVID," Mrs. Obama, 56, told Conan O'Brien in an appearance on his talk show in September. "There were sort of the early stages where we were all excited to be together and we were being all organized and we would spend the days apart doing our respective work, the girls were still in classes in the spring, so we would be working and then doing a little exercise and coming together in the evenings and we would have these activities" like puzzles and games and an "art exhibit day."

But then the pandemic kept going and "our kids got a little sick of us, which was fine 'cause we were pretty much sick of them," Mrs. Obama told O'Brien, adding that a move to their home in Martha's Vineyard in the summer gave them "more room to roam around."

"And now the kids are back in Zoom-land with classes. They're doing it remotely," she said in September. "And they're no longer thrilled about being with us." (She said, laughing, "They'll come down periodically for a grunt.")

Barack, Michelle, Sasha, and Malia Obama
From left: Barack, Malia, Michelle and Sasha Obama in 2016

President Obama echoes that sentiment in his conversation with PEOPLE.

All the togetherness “doesn't mean that we haven't gone through what I think a lot of people go through, which is a little bit of cabin fever," he says. "And I'm sure the girls have felt it more severely than Michelle and I have.”

• Watch the full episode of People Cover Story: Barack Obama on or download the PeopleTV app on your favorite device.

While Malia and Sasha have been taking classes, the former president was finishing the already-bestselling A Promised Land, which he dedicated to his wife and daughters.

"As I write about, there are great joys during our time in the White House. There was never a time where we didn't recognize what an extraordinary privilege it was to be there," he tells PEOPLE. "I think most importantly, our children emerged intact. And they are wonderful, kind, thoughtful, creative — and not entitled — young women. So I think that's a big sigh of relief."