Specific am3 processor in an am2/am2+ mobo

I have a Biostar A770 a2+ AM2/AM2+ motherboard and a bunch of other parts that I'm turning into a computer for grandpa to surf the web, and I just need a cheapo processor to go in, the cheaper the better. I see a $39.99 + shipping am2 processor on newegg, but I also see this $36.99 free shipping AM3 processor which saves $9 including shipping.

I've read that AM2/AM2+ motherboards are, to a certain extent, forward compatible with AM3 processors but I would like to know if the specific motherboard that I have will be pnp compatible with the AM3 processor or does it depend on how recent the bios is, because I dont know. up until september I used that motherboard with an athlon 64 x2 6000+ just fine.

1. Will I be ok?
2. Do I need to include more information?
3. Should I just take one for the team and shell out the extra $9 for a better chance of working and losing the possible better performance and money?