Absolutely.
These cars go 200K without breaking a sweat with normal maintenance.
Change the oil every 5k, and go in for your free oil change at 15k. It's extremely important that the car gets at least one oil change in between BMWs scheduled oil change intervals.
At 100K miles with 15k intervals, the goo/buildup in the motor has done it's damage. The VANOS system (adjustable cam timing) is all reliant on tight tolerances, and oil PSI.
Oil change every 5k, (or at least 7500) is cheap insurance.
I've owned probably 15-20 of these cars. Still have my '88 325ix with 190k on it. And my '02 M5 with 50k.
I wouldn't drive anything else