As long as you cast a spell with rebound from your hand, rebound will work regardless of whether you paid its mana cost or an alternative cost you were permitted to pay.
Sight Beyond Sight
If a spell with rebound that you cast from your hand doesn’t resolve for any reason (either because another spell or ability counters it or because all its targets are illegal as it tries to resolve), none of its effects will happen, including rebound. The spell will be put into its owner’s graveyard and you won’t get to cast it again on your next turn.
If a replacement effect (such as the one created by Rest in Peace) would cause a spell with rebound that you cast from your hand to be put somewhere other than into your graveyard as it resolves, you can choose whether to apply the rebound effect or the other effect as the spell resolves.
Magic: The Gathering · ™ & © Wizards of the Coast · Illus. Anastasia Ovchinnikova
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