I asked this same question 3 years ago and was told it could cost anywhere from $50 to $1,000,000. I couldn't get the person to budge their estimate for a 'simple' app. I talked to a few digital agencies and looked at freelancer sites but there the range was huge. I then took an intro course on iPhone/iPad development, learnt to code to an intermediate level, built and put an app on the App store and help teach that intro course. I now know the $50 is more absurd than the $1,000,000 estimate. I agree with many of the excellent answers above. In particular, you haven't provided enough information to get an accurate measure of how much the app will cost. Some developers will tell you it will cost $1,500 to $2,000 per screen but the reality is that it depends on what is happening behind the screens (database?, payments system?, login, security issues?). Designing simple elegant apps with great UI/UX takes real skill and usually require lots of iterations based on customer testing and feedback. Everyone should start with an MVP and customer testing and feedback. Once you build the final app, you need to maintain it as new devices come out and operating systems change every year - so make sure the code is well written in case it needs to be taken over by someone new. This is more a risk when user offshore freelancers - I've heard lots of horror stories. That said, I can think of a couple of ways to save money:
I've play around withhttp://howmuchtomakeanapp.com and while I think it produced some higher than expected costs, it wasn't out of the ball park. Building high quality, robust apps is expensive. I would be very suspicious of someone telling you that it only costs $500 to build an app unless it was the type of app that just displayed static data on screens.
** Recently saw presentation by Gigster who say that can quickly and accurately quote development projects based on their experience and proprietary database of projects. I would get them to give you a quote.