The age of consent in New Hampshire is 16. However a close in age exception exists where a person may "engage in sexual penetration" with a person older than 13 but younger than 16, but only if their age difference is less than three years. However if the partner is acting "in loco parentis", e.g. as a teacher or a guardian, the minimum age is 18.
Also, IMO, any parent that consents to their 13 year old having sex does not deserve to be a parent. It doesn't matter how much birth control you use, the only 100% effective method is leave it in his pants. And at 13, you are way too young to be taking even the slightest chance of getting pregnant.
Another thing to think about: There is also the reality that at 16, he will brag about it to his friends (I was a teenage boy once, and I know this for a fact). Do you really want to start off high school with a reputation of being "easy"?