Before anyone jumps to conclusions I havent dated or slept with a 16 year old etc Im posting this because I want to gather some opinions. I added her on facebook and we have been speaking a little bit.
4 years starts to not be that big of a difference when you get older so my advice is to wait until you are at least 18.
In the end, they accepted it since they like her, though.
I've been through two serieus relationships (one two years, other one and a half years) and I'm her first boyfriend, even one of the first guys she ever talked to.
She's young, so she's going to want to be free and be able to experience new things.
On top of that, you're 20 and she's 16, so there IS a matter of maturity levels here.