I've PM'd dozens of mobile applications, all with vary degrees of complexity, cost or resource requirements. There are several details that need to be worked through (including whether or not you're open to a non-native mobile app); but at that price range I would suggest (tho reluctantly) to consider a solution such as Upworks/the website formerly known as E-lance (as suggested by others.) Alternatively you could consider posting a job board for your local college's IT program to get an intern-type programmer who can step in and help build things out.

That being said, before you explore those or any other route you really need to do your diligence and invest time into really documenting/scoping your app (you're going to need to make this as completely detailed as possible to help reduce upfront costs and remove ambiguity from your prospective partner.) I would recommend going through a process of writing your technical/functional specifications document (which can include all wireframes, information architecture, user stories and third party integrations.) If you're looking for support or guidance on how to structure this document and create the materials you need, or explore development options out there available to you, feel free to schedule a call and I'd be happy to help!