You don't understand brand value.
Make no mistake, this is a crazy amount of money spent on a less then 2 year old, 13-man company. I think post-IPO, Mark might not have been able to get this as easily approved by the board of directors.
Of the four engineer/developers, only one of them wasn't hired in the last few months. One of them was hired two weeks ago, one in January, another in December.
So only one developer is responsible for the app and all the servers, the others haven't hardly had time to get up to speed.
Not surprising, the iOS version is trivial since CoreImage' image processing library provides all the filters and image processing. Doing the port to Android was the hard part, although most likely they just licensed an image processing library from someone, or extracted it from GIMP's open code.
I think it is realistic to say the cost of developing the iOS version, which is what most of their 30 million customers are using, was well under $100,000.
But secondly, I'm not sure how you went from 13 people to 3, lets assume we we accept that we are only talking about the 3 people. Even if those 3 people are making only $50k yearly salary, working on this for 6 months is already costing Instagram well over $100k once you take into account office space, benefits and hardware.
The success of these new things like Instagram and Tumblr seem to be their mindless simplicity.
Mentally, I lump Instagram, Pinterest and other en-vogue social-ly apps together. Speaking of the latter, I would imagine they're probably rubbing their hands with glee right about now.
Edit: I don't mean to rubbish what you're saying. I agree that it and the brand have value but to me that equates to something like $150 to maybe $250 million at a push. $1 billion is off the wall.
Edit 2: as is a $100 billion valuation for FB.