How does one show that the inclusion of circle in the punctured plan is not null bordant?

Question

Let $(S^1,i)$ be a singular manifold in $\mathbb{R}^2-\{ 0 \} $ where $i$ is the inclusion map. I understand that this map is not nulhomotopic, but am unable to show how to prove that this is not null bordant (it seems to be that way from intuition). Could someone please suggest some line of approach ?