The # HM47200 would indeed adapt your existing 4 pole to a 7-way blade-style trailer connector. In that respect, it would work just fine.
However, I typically recommend going with the # 37185 instead, as the adapter also offers a 4-pole connector. If your trailer doesn't have or need trailer brakes or a need for a 12-v power supply, you'd simply plug the adapter into your existing 4-pole, and ground the white tire to the vehicle frame. This will provide you with lighting functions, and... view full answer...
The best trunk mounted bike rack that fits your 2014 BMW 640i convertible that also happens to fit your budget is the Thule Passage part # TH910XT as it has an easy to install design loaded with great features like shock absorbing frame cradles, adjustable arms, and a wide arching design that fits vehicles easily.
If you plan on carrying any women's or alternative framed bikes without horizontal top tubes you may also be interested in purchasing a Kuat Bike Frame Adapter Bar # UB01 to... view full answer...