。
I'll be seventeen next year.
Literal
Next-year [at-で] 17-year-old [into-に] become-[explanatory-んだ].
来年で ('as of next year') uses で as a temporal cutoff, marking the reference point at which the age becomes 17. んだ (casual のだ) frames this as a piece of shared information — 'I'm turning 17 [you should know].' Note the plain form だ vs polite です — this is casual speech.