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The 330e is a plug-in hybrid (PHEV), so it has a petrol engine and a smaller battery pack than a full EV (which runs exclusively on battery power). That means the BMW’s battery should be less expensive to replace if it ever needed to be.
At the moment, the world is waiting to find out how long EV batteries last, but it’s looking like between 10 and 20 years is going to be the magic number. A lithium-ion battery like this one will last longer if it’s never over-charged and is cycled regularly rather than left sitting for long periods.
There are two likely suspects here. The first is a blown head gasket which is allowing the oil and coolant to mix. Sometimes this shows up as oil in the coolant, sometimes as coolant in the oil. Sometimes both.
But before tearing the engine to pieces to change the gasket, it’s worth checking if the car is fitted with either an engine or transmission oil cooler. These often use the engine’s coolant to keep the oil or transmission fluid cool, and a failed one can allow the two fluids to mix, showing up as oil in the radiator or header tank.