Functional Programming style in F#
It looks good! Just a couple of points.


Instead of


let data = sr.ReadToEnd()
data



you can write

sr.ReadToEnd()

sprintf is more idiomatic than String.Format.
displayExchangeRate would be better written as a loop or using
List.iter (or Seq.iter).
DataContractJsonSerializer.WriteObject uses Encoding.UTF8, but you're decoding with Encoding.Default, which returns the OS's current ANSI code page.