Is the battery covered for more than a year if you extend the warranty?

[noxxle]

I've noticed for laptops that even if you purchase an extended warranty, the battery is usually limited to the first year. Is this the case with the Reader?

Many people have told me that in general, after about a year of use, lithium batteries tend to lose their charge pretty fast. Is this true?

How much does sony charge to replace the battery? I noticed that Kindle batteries are only 20 bucks.