Is there a single word that means "next year"?
Solution 1:
There’s twelvemonth, which:
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Sometimes was written as a single word
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In some contexts meant “next year”
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Probably met both of those criteria in Early Modern English. In any case, there are plenty of examples from Middle English, such as this one from Rolls of Parliament (1429):
... paiable atte Cristemas come Twelmoneth. (“payable at Christmas come twelvemonth”)
(This word still appears in some dictionaries defined as “one year” though I have never heard it used before.)