How much do multiple weapon enchantments cost?

If I were to enchant a composite longbow with two +1 enchantments, how much would it cost?

I have a masterwork longsword (315gp). I want to add the magic enchantments Keen and Bane to it. Both of those enchantments are a +1 price of 2000gp each. Would it cost 4000gp to enchant the longsword or would it have the cost of a +2 enchantment of 8000gp?

Special properties are priced as if you were increasing the enhancement bonus of the item by that amount. So a +1 keen longbow costs the same as a +2 longbow and a +1 keen bane longbow costs the same as +3 longbow. All magic weapons must have at least +1, so a keen longbow or keen bane longbow would be impossible. Enhancement bonus costs scale quadratically, $bonus^2 \times 2\,000\text{ gp}$. So +1 is $2\,000\text{ gp}$, +2 (or +1 keen) is $8\,000\text{ gp}$, and +3 (or +1 keen bane) is $18\,000\text{ gp}$.

These rules are stated in the section on magic weapons:

Special abilities count as additional bonuses for determining the market value of the item, but do not modify attack or damage bonuses (except where specifically noted).

A weapon with a special ability must also have at least a +1 enhancement bonus.

• Since it has multiple enchantments on it, equaling the price of a +3, can it hit monsters that can only be hit/damaged with +3 enchantments, or that's just a cost thing, not a damage thing? Aug 7, 2016 at 3:07
• @JesseCohoon To my knowledge, there are no such monsters (DR pierced by specific amounts of enhancement bonus died in the 3.0 to 3.5 transition); what you may be thinking of is Pathfinder’s rule that allows higher enhancement bonuses to pierce DR normally vulnerable to certain materials and/or alignments. Assuming that is what you mean, then no, a +1 keen bane weapon would not pierce that. In general, it is just for calculating the cost. Aug 7, 2016 at 3:28
• KRyan is correct, only the actual enhancement bonus allows you to overcome additional DRs, not the 'effective' bonus used for special quality pricing calculations. To bypass DR/adamantine you need a +5 weapon. Aug 7, 2016 at 3:42
• Correct. The equivalency is only for price. Aug 8, 2016 at 4:12
• Note that because a bane weapon does count as having a higher-than-usual enhancement bonus against certain creatures, it might actually count as being able to ignore the DR of those creatures as if it had a higher enhancement bonus... Maybe. The interaction of those two rules elements is open to debate. Aug 13, 2016 at 10:53