Am I at serious fault for send an inappropriate pic to a 16yr old?

Was talking to a girl who i thought was 18 about a month or 2 ago(haven't talked to her since) turns out she was actually 16. She kept insisting that I send her a nude photo of my private part and I kept saying no until after so long I finally sent it. Today " her dad" called me saying his wife wanted to press charges and what not but he didn't want to because I'm military so we talked a bit and the final solution was he's sending his daughter to counseling but his insurance wouldn't cover it unless a police report was made and he didn't want to do that. So he came up with the class is $2000 he wants me to send him half and he will pay half, do I cough up the money and hope he keeps his word? And is it a really serious crime that a minor bugged me for a pic and I sent one? She also sent a bikini pic to me that I didn't ask for and I deleted it immdiately because i did not ask or pressure her into sending anything. Please help me out sorry was so long.