0. Have you looked at other ways to save money that could give you more bang for your buck? $20 per month often isn't a lot compared to overall cashflow, and if you could save more by cooking more and going out to eat less or something, you may want to focus on the larger savings first.
1. Is electricity also included in your rent? If not, that could offset your savings.
2. How much power does the induction burner you're looking at pull? The ones we have take a lot of juice and could trip a breaker if we aren't careful.
3. Do you do any baking? I'm guessing not based on your low usage.
If the answers to those don't change your calculations, I say give it a try. It would be an interesting experiment, at least!