Abel,

My AMA card says right on it: "Expires December 31 of the Above Year"

If there is indeed a grace period, it's news to me. I would imagine that since the insurance is a provision of membership, that it would carry over too, though.

Regardless of the exact date of expiration, your membership is still only good for a period of 1 calendar year. Waiting to renew doesn't make your membership last longer or save money.