Yeah your math totally makes sense. I just disagree with the premise:
> The life of an engineer is a life if sacrifice and 7 days a week work for five days pay.
This just isn't true. Maybe at certain startups, but it's your choice to work there. As a (qualified) software engineer, you're blessed with thousands of options, many extremely comfortable. Flexible hours, free food, great pay, no dress code.
When so many people are struggling just to make ends meet, I have very, very little sympathy for someone in shams' situation. Just get a new job.