Metamagic Burning spell and acid arrow

Question

I am wondering exactly how the metamagic feat burning spell and a spell like acid arrow interact.

Burning Spell +2 spell level

Benefit: The acid or fire effects of the affected spell adhere to the creature, causing more damage the next round. When a creature takes acid or fire damage from the affected spell, that creature takes damage equal to 2x the spell’s actual level at the start of its next turn. The damage is acid or fire, as determined by the spell’s descriptor. If a burning spell has both the fire and acid descriptor, the caster chooses what kind of damage is dealt by the burning spell effect.

Acid Arrow Spell level 2

An arrow of acid springs from your hand and speeds to its target. You must succeed on a ranged touch attack to hit your target. The arrow deals 2d4 points of acid damage with no splash damage. For every three caster levels you possess, the acid, unless neutralized, lasts for another round (to a maximum of 6 additional rounds at 18th level), dealing another 2d4 points of damage in each round.

Say the spell is cast at caster level 7, which allows acid arrow to take effect for 3 rounds. The round it hits it does 2d4. The second round is 2d4 + 4 from burning spell. Now does the spell only do 2d4 or 2d4+4 on the 3rd round? Does it deal another 4 on the 4th round since the spell would have finished but the wording of the feat suggests it lingers?

Answer 1

When a creature takes acid or fire damage from the affected spell, that creature takes damage equal to 2x the spell’s actual level at the start of its next turn.

This means that, for each time the target takes damage, it will take 4 points of acid damage on its next turn.

So let's assume you cast Acid Arrow at 9th level, the minimum necessary to apply the metamagic and a number divisible by 3 to ease the math. That means your Acid Arrow will last 4 rounds (1 plus 9/3):

• Round 1: 2d4 damage (direct hit)
• Round 2: 2d4 + 4 damage (on going effect)
• Round 3: 2d4 + 4 damage (on going effect)
• Round 4: 2d4 + 4 damage (last round of on going effect)
• Round 5: 4 damage (burning spell)

Multiple Hits

Few spells can actually cause acid damage more than once per round, but Prismatic Spray has a small chance of doing so.

In that case, if the target is hit twice, you simply double the damage next round.

Cantrips

Being effectivelly a 0 level spell, Acid Splash would be a waste of a 2nd level slot, unless we increase it to a 3rd level slot using Heighten Spell. But again, there are better options for a 3rd level slot than 1d3+2 damage.