Long answer: If you want to teach, or else work in a branch of scientific computing or algorithms research, a Masters or PhD are excellent (and generally vital) paths! They may also be helpful if you learn best through guided study.
However, if you are an independent learner, and just want to be some form of a programmer/software engineer/software architect/{insert other fancy HR-coined term here}, there's no need to spend the extra time and money. Outside of the aforementioned fields, a Masters or PhD has fairly limited value for the price. Sure, you'll find some jobs open that you wouldn't otherwise, but not as many as you would think, and not necessarily better paying either.
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Short answer: NO
Long answer: If you want to teach, or else work in a branch of scientific computing or algorithms research, a Masters or PhD are excellent (and generally vital) paths! They may also be helpful if you learn best through guided study.
However, if you are an independent learner, and just want to be some form of a programmer/software engineer/software architect/{insert other fancy HR-coined term here}, there's no need to spend the extra time and money. Outside of the aforementioned fields, a Masters or PhD has fairly limited value for the price. Sure, you'll find some jobs open that you wouldn't otherwise, but not as many as you would think, and not necessarily better paying either.