Why have you decided not to have a formal lease? A verbal agreement isn't worth the paper it's written on and all that. Even with (or especially with) family members there can be misunderstandings. A formal lease should make everyone's obligations clear, what the rent is, who pays for what, who is responsible for what, under what circumstances the tenant must leave etc. I think it is in everyone's interest to do this. If you are worried about fixing a term on the lease, that can be addressed in it with a break clause setting out what notice is needed by either party to terminate the lease.
Just my opinion but so easy to have a falling out without it and as a family member is involved, there is more than money at stake.