Today's Maths Question (TV Licence based..)

linzeloo2

Good morning All,
I'm hoping someone may be able to assist me with this as my head is now hurting trying to work it out.
We are a household of 3 sharers. We set up a TV Licence in my name to cover our TV valid from 15th June 2019, 5 monthly payments of £30.90 started on 15th July which we equally contributed to (last payment is 15th Nov before it drops to £12.87).
One housemate is moving out on the 9th of November and a new roomie is moving in on the 10th - I can't for the life of me work out who owes what now.
Please help before I self combust.

tempus_fugit

Each person should just pay their share up until they move. Then the new housemate can pay their share of the next payment, which would be the one on the 15th November. No point in trying to do a pro-rata on the number of days each person is resident, IMO, but if you want to then the maths is pretty simple, multiply their share by the number of days they are resident and divided by 30 or 31.

Cornucopia

If you're trying to be extra fair to your departing flat-sharer, then you need to factor in the double payments that you have been making since June. Half of the payments go to build up a credit covering the next 6 months licence.

The easiest thing is to probably cancel the Licence, share the refund and start a new one. Alternatively, get the new flat-sharer to pay the departing one an amount equivalent to their refund share (which should be one third of half the annual cost, or, £25.75).