If this means "will demonstrate" then surely the final "a" should have a written accent? Is this a mistake or have I misunderstood something?

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1

If this means “will demonstrate” then surely the final “a” should have a written accent? Is this a mistake or have I misunderstood something?

2

It’s past subjunctive, not future. Imperfecto de subjuntivo.

El campesino decidió darle otra oportunidad para que el árbol demostrara su fertilidad.

“decidió” means “he decided”, and indicates the sentence is in the past. Then after “para que”, one must use the subjunctive. Since the sentence is in the past, one must use past subjunctive. Hence “demostrara” without accent.

Note that past subjunctive has two possible forms, one could also say “para que desmostrase”

3

Thanks for helping me with this excellent reply!