Apple Care

Hi,

I purchased a new iPhone (paid full) on May 30th. My phone started to restart every few minutes so I took it to Apple and they gave me a new iPhone on June 15. I had purchased Apple Care for the first on June 9th and now with this new iPhone they gave me, it is asking me if I want to purchase Apple Care! My question is, can my Apple Care be transferred to my new phone? I think it would be unfair that I had purchased a new iPhone paid in full and then have it malfunction and end up given a new phone as replacement and my apple care of $80 go to waste!!! Please can someone help.