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Via AirfareSpot there are fares from New York, Chicago, and Washington DC to Munich from $437 roundtrip.
New York and DC fares are available in December (before the holidays) and January through March. Chicago is available just in December.
Beer garden restaurant outside Munich, copyrightkzenon / 123RF Stock Photo
And all of these fares are found using airfare metasearch site Momondo.
You can credit the miles for these trips to Singapore Airlines KrisFlyer and earn more than you would any other way.
While a non-elite MileagePlus member crediting United flights to the revenue-based MileagePlus program will only earn 5 miles per dollar on the cost of the ticket excluding taxes, nearly all United fares earn 100% of flown miles when crediting to Singapore Airlines KrisFlyer (.pdf). That means you earn about 5 times as many miles with Singapore Airlines KrisFlyer for your trip flying United than you would crediting to MileagePlus.
While Singapore miles do expire after 3 years (not 3 years of inactivity), you can top off a KrisFlyer miles account with transfers from American Express, Chase, Citi, and Starwood.