Our London house swap saved us money. The bigger payoff was watching my teenager grow up.

I was enjoying lunch with a friend during my summer vacation in London when she asked about the whereabouts of the rest of the family.

My husband and tween son were at a museum, I told her. I said I wasn't sure about my daughter, then 15. I explained that we'd parted ways earlier that morning, and she was exploring the city alone.

She'd already spent time going to places on her own, partly because she no longer shared the same interests as us.

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Her idea of fun was shopping in clothing stores and browsing street markets like those in Camden and on Portobello Road. We were more into seeing the sights.

It was good to see her so happy. We live in suburban New York, which can be cloistered, and she could spread her wings in the British capital.

The trip came about via a house swap with a former colleague who lived in the Haringey area of London. Her family moved into our house for two weeks, and we stayed in theirs for seven days before visiting my parents in the north east of England.

It was a win-win: we got a taste of inner-city living, and they experienced New York. The accommodation was free for both parties, and they fed our three cats while we were gone.

I never imagined the added bonus of my teenager gaining independence during the exchange.

She was already pretty street-savvy in Manhattan, since we live about 50 minutes away by train, and she would go with friends.

This felt different. She was in a foreign city, albeit a relatively safe one, where people spoke English. She was unsure of the Underground and bus systems.

Then there were the cultural differences, such as standing in line for almost everything. Or something as simple as being understood when she asked for half-and-half.