Need help determining pricing for designing a very ambitious app

I know its alot but please read all of it so you can fairly assess the situation!

The Important Backstory

I am a 17 year old self taught user-experience designer that is pretty far ahead in the field (or so I would like to think). I believe this is relevant since this is how my client found me - http://ift.tt/1Au2U4C is a link to some/most of the work I have done completely on my own (mainly at the age of 16). Not too long ago I started a pretty ambitious project of my own where I was actually conducting a fully fleshed out UX case study (research, personas, wireframes, etc.) as well as reading front to back "A project guide to UX Design" by russ unger and carolyn chandler which has been a very good guiding support to doing real research about every action and element of an app rather than self-designing what I would want to use while keeping functionality highly in mind but no real wireframes or research was done. After starting this monumental project (for one person atleast) I have quickly jumped drastically in my understanding of just what is a good user experience and what is actually functional for the demographic and not just throw a hamburger icon here. At this point I would say I am about 1 year into an associate degree in UX (or again as I would like to think). I have formed my own hypotheses on everything that I have been putting into this hypothetical app and am heavily citing the reasons I chose one thing over another. The bad part about this is that it has not been completed yet which could very easily lead people thinking me to be less truly experienced.

The problem

I have recently been contacted by a client who has already done a decent amount of thinking when it comes to the app (many pages of notes on services etc.) that he wishes for me to design - quite startup-y. The app is probably past the normal level of ambition and midway to quite (quite is the max on my made up ambition level). We have talked for about 3 hours on just what the app is/does and what its goals for the user are. I have another meeting online with him this friday where we will discuss the core functionality of the app (my hopes for this are to be able for me to make a bulleted list in my notebook for the screens and each feature that will be seen and interacted with on them. My priority would be the ux while others (client has other members for all other areas of the project). The client has already been apart of the making of another app that I will not list for confidentiality purposes. Needless to say, the app is more impressive than I would have thought after a quick glance, in terms of looks and feel (with some improvements that could be made with monetization that I brought up to the client) because I couldn't say how good it is without the analytics and user research. The budget discussion has been postponed until I affirm that I have all the necessary information of what designing the app would be ie. screens, functions, services, research, etc.

I do not know what I am valued at being that I am 17 and self-taught but no absolute real world experience of the business side of deals like this (I've designed some banners and etc. for people on twitch and youtube before but that was just like $30-$50 paypal transactions). It is also a gigantic amount for one person to do especially with the quality that I want to do it in (although I think the client would be fine with something like that from some of the projects linked from my behance that were just designed and not fully and excessively thought out but with functionality in mind).

I read this a while back but was not touching upon the entirety of this project and all that it entails. What do you think a fair price would be for me to charge given my experience? I know I would definitely be getting a contract for it too so I might need something a little more detailed than the Shake app (or not). Or do you think I should pass up the opportunity because of my lack of real world experience and/or age or naivety?

I feel like there are probably some crucial elements to the story that I am forgetting to put in because of my roaming brain so please comment if any more info is needed and I will respond or edit the post to have it in it.

Thank you to anybody who read all of this and double thanks to the people who read it all and reply with help!