Rent increase for inherited tenants at low rents

[Yulia J.]

We've just got a triplex. My family and I are living in 1 unit, and we inherited month-to-month tenants in the other 2 units. They've been renting here for 7 years or so, no trouble. Their rent is very low  - they are paying $760 and $780 while market rents for units like those are at $1,000 in their current condition, and they go for $1,200 if updated. We want to keep the renters as they are already here and paying, we would just offer a 9-12 month lease.  I am thinking to meet in the middle for now -  that would be a $110 instant increase -  and tell them that there will be another increase in 9-12 months. 

How would you go about it?