Long term tenant way below market rent

[Alex Alleva]

I recently completed the buy out of my family members on a quadplex. We had tenants that have been renting from my family for roughly 12 years. They are great and give zero issues. The only problem is my grandparents never raised their rent over the years. They are now paying roughly 600-700 under market value. I clearly need to raise rent but feel bad jacking it all the way up. They were always good to my family and the husband has been sick and not working for a few years now but they have never missed rent. I am thinking about raising rent $100 and telling them that it will go up another $100 in a year. 

What does everyone think? Am I just shorting myself and caring to much for my tenants?