You don't need one. But, I've found that wearing one helps me to see just how hard I'm working when I'm training.
This is my heart rate monitor that I wear on my wrist:
And this is the strap that is worn around the chest:
For an aerobic workout, to build fitness, you want to aim for 60 to 80% of your predicted maximal heart rate (PMHR). Your PMHR is approximately 220-age.
So, for a 50 year-old person, PMHR is 170 beats per minute. The target range for a workout should be 102-136 beats per minute. You can allow your heart rate to go higher, which would put you into the anaerobic phase, using more glycogen for fuel than fat.