what does it cost to replace/repair battery on iPod 5th ten?

This was purchased in late 2012. Battery does not hold a charge like it used to - now lasts about 2-3 days while basically not being used. But it does re-charge - and very quickly. From past experience, all of this means the battery is reaching the end of its life. My last iPod (a 2nd gen) lasted about 18 months and started doing this. I had Best Buy extended warranty and they replaced that device - no questions asked - indicating that was a common lifespan for the device. Foolishly I did not purchase Apple Care when I bought this one :-(. I have a fairly new iPhone so I am wondering if I should just let this one die, or try to repair it. What is the cost of a new battery for an iPod 5th Gen?