Kinvey have a new infographic on "How long does it take to build a mobile app". The premise is that it takes, on average, 10 weeks for the server side and 8 weeks for the phone side. While this is very simplistic, I concur that 2 months is roughly the average time I have spent on the first version of non-trivial apps. In practice, the time depends more on how many different clients (OS platforms and phones on those platforms) have to be created and the degree to which they have to be tested. Also, the server side is usually done at the same time as the client so the elapsed time usually tends to be the greater of the client of server development times.
Another aspect people don’t think about is how well the app has to be developed. It’s possible to cut corners and develop quicker. Sometimes this is intentional if a ‘proof of concept’ or demo is required but other times a poor choice of developer can also result in poor implementation. This can result in apps that meet the immediate need and cost but cause a technical debt. For some kinds of apps, such as advertising or marketing apps, that are one-offs, this might not matter and be desirable to reduce costs. It all depends but I urge you to at least think about is how well you want your app to be developed.