If you bought a retail AMD-boxed version of the CPU it should have a multi-year warranty in any event. If you bought an OEM version it may not, and then the additional warranty might have some value.
Unless you are overclocking or otherwise messing with your PC, then in my judgement a one year warranty is a waste of money - the CPU's are made to last for years and years in even poor environments.
Usually these point of sale warranties, service contracts etc. are way overpriced and are aimed at unsophisticated or subserviant shoppers. The proof of this, and the reason they are pushed so hard by many vendors on all sorts of merchandise nowadays, is that often they are the most profitable "product" the stores sell !!! OTOH, if the vendor has a no questions asked replacement policy, then the warranty might be worth it with some kinds of items.
The only time I personally buy these things is if I know I'll beat up the item and maybe break it, like my Walkman and portable CD player I use while skiing or mountain biking.
I bought a TV recently and after 2 weeks it stopped responding to the remote. I took it to a repair shop and they fixed it under the manufacturer's warranty at no charge to me. The cost of an extra warranty by the vendor would have been a waste of money in that case.
If you use your credit card for purchases you may also have protection under their buyer protection programs too.