How to convert date format from dd/MM/YYYY to YYYY-MM-dd in swift

I tired to covert from 21/07/2016 to 2016-07-21 but got this date 2015-12-20
Here is the Code that i have try

let inputFormatter = NSDateFormatter()
inputFormatter.dateFormat = "MM/dd/YYYY"

let outputFormatter = NSDateFormatter()
outputFormatter.dateFormat = "YYYY-MM-dd"

let showDate = inputFormatter.dateFromString("07/21/2016")
let resultString = outputFormatter.stringFromDate(showDate!)

print(resultString)

How to convert?
Thank you

First changes your year formatter with yyyy and instead of using two NSDateFormatter use just one like this

let inputFormatter = NSDateFormatter()
inputFormatter.dateFormat = "MM/dd/yyyy"
let showDate = inputFormatter.dateFromString("07/21/2016")
inputFormatter.dateFormat = "yyyy-MM-dd"
let resultString = inputFormatter.stringFromDate(showDate!)
print(resultString)

For Swift3 and later

let dateFormatter = DateFormatter()
dateFormatter.dateFormat = "MM/dd/yyyy"
let date = dateFormatter.date(from: date)
dateFormatter.dateFormat = "yyyy-MM-dd"
let resultString = dateFormatter.string(from: date!)
print(resultString)