Several sites can confirm that your VIN is an R27 number, which ranged from 372001-387354. But to find out exactly which year BMW made that number, you have to ask the BMW Archivist at:
historisches.archiv@bmw.de
BMW used to look up the history of a bike for free. I think they will still tell you the year for no charge. Several years ago I was interested to find out that my R27, which I picked up at the factory in 1966, was actually made in 1964. I wonder where BMW kept it for two years.
In the past few years the Archivists received so many requests for information that BMW began offering a official banknote quality Certificate of Origin, available for $90 through your dealer, giving:
Name of Current Owner
Vehicle type
Chassis number
Production date
Delivery date
Original Color
Dealer or importer, where the vehicle was delivered to
Stamp of the Historical Archives
Signatures of the head of the Historical Archives and the person
responsibile for the vehicle.
If the Archivist replies to your request for the year, the message may contain info on how to apply for a full Certificate. There is a PDF form to fill out.