I made an attempt to check train schedule from Munich to Murren and did not get a price. Will a train pass get you from Interlaken up to murren?
A Swiss pass, Swiss Transfer Ticket, Swiss Card, Swiss Flexipass - ALL will get you from the border of Switzerland all the way to Mürren.
And a Eurail Pass or other multi - country pass will get you as far as Interlaken, with a discount after that, buynyou 'll have to buy tickets.
If you book sufficiently far ahead using the German Rail website, you can get a Europa-Spezial Schweiz ticket for €39. This ticket includes not only rail by various routes from Munich to Interlaken Ost but the trains from Interlaken to Lauterbrunnen and Mürren. When booking, spell Mürren with the umlaut or Muerren. If you spell it Muerren, the Bahn will offer a selection including "Mürren BLM".
Well that would definitely be the way to go...