In a house with 3 shared ownership, one moves out and the other assumes payment. How do we determine a fair payment amount to the person that moved out? The 2 were a married couple who put down 50% of down payment and the third party put the other 50% down payment. In a matter of 2 years the third party moves out. The house is being sold for $150k more than what the initial cost of the house was. Is there some type of formula to figure out a fair split?
Without any other sort of agreement in place, they own the amount of equity that they did when they first purchased the house, according to how much of the downpayment they spent. Changing the amount paid on the mortgage changes nothing, the lender is only concerned that it gets paid, but doesn't care who pays it.
If all parties agree it can be fair to make adjustments in equity based on the amount paid towards the mortgage, but that should be agreed on in advance. The fairest agreement would still end up being approximately 50% for the couple and 50% for the third party, because even though the couple was paying the whole mortgage for several years, that is effectively equivalent to them paying half the mortgage and the other half in rent to the 3rd party (who then forwards that towards the mortgage). If it was a standard mortgage and the payments were approximately equal to what the house could rent for, the 3rd party getting 50% is as fair as it gets.
If the house could be expected to rent for significantly more than the mortgage payment in its market (on average throughout the years the 3rd party didn't live there) it would be fair for the 3rd party to receive a bit more than 50% since a little more than half that mortgage payment can be thought of as having been forwarded through the 3rd party.
If the house could only be expected to rent for significantly less than the mortgage payment (again, on average throughout the years the 3rd party didn't live there) it would be fair for the 3rd party to receive a bit less than 50%.
Either way, 50% for the couple, 50% for the 3rd party, is pretty close to a fair situation. Remember though, what's fair doesn't matter, it's what was agreed upon that matters (see paragraph 1).
The couple payed 50% of the mortgage for 25% of the time of ownership, and 100% of the mortgage for 75% of the time. Thus, morally, they should get
50% * 25% + 100% * 75% = 87.5% of the profit.
But that might not be what the law says.
EDIT: I'd be interested to know why it was down-voted.