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Yes, indeed, there is a time frame. For this year (Class of 2020), from the College Board website: “Only scores earned on administrations of the SAT or ACT from August 2017 through December 2019 will be considered by NMSC. NMSC will not accept scores from a test administration taken earlier than August 2017 or later than December 2019.”
For Class of 2021, this would translate to:
August 2018 to December 2020.
So, yes, scores from way back in Aug 2018 should be good, and for sure, anything more recent or going forward is good. Definitely do it sooner rather than later if your kid is in the NM zone, to allow for re-testing if something goes sideways on test day!