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"Singing teacher Miri Gellert is nearly 30, has lived at home for the past nine years (Vs. for the last nine years) and has had her share of awkward encounters." (BBC)

Is there a difference between 'past' and 'last' in this context?

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There is a difference. With for the past nine years the reference time can be to now or then.

I have lived here for the past nine years.

I bought this car when I lived in Boston. I was a college student at the time and had been in the city for the past four years.

But for the last four years, when unqualified, is spoken only with reference to now, not then.

I have lived here for the last four years.

I bought this car when I lived in Boston. I was a college student at the time and had been in the city for the last four years. ungrammatical

But if the phrase is qualified, it means final (four), and then it can be used in reference to then:

He died in New York and had worked on Wall Street for the last four years of his career.

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Nowadays it seems to be no difference between the two. Subtle differences (if any) are discussed here: https://english.stackexchange.com/questions/3986/in-the-last-3-months-vs-in-the-past-3-months

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