What's fair varies from person to person. Here are some of my thoughts about your model.
Your model did not consider that not all €100 from your partner goes to the Principal Portion of the Monthly Payment.
For example, in a loan of 100k for 25 years, in the 1st month, only 61% of the payment goes to Principal Portion. The rest goes to Interest Portion. In the 12th month, only 62% of the payment goes to Principal Portion.
Your model simply provides interest-free loan to your partner, while you are paying the whole portion of interest to the bank.
The correct way to track the Principal Paid / Total Principal is using Amortization Table.
- You bought the property in Jan 2012 for €100k at 2% interest for 25 years with 0%. Monthly payment is €423.85.
- Your partner joined you in Jan 2022 and start paying you €100.
- In Jan 2022, the principal portion is €314.08 of €423.85 (i.e. 74.10%). Therefore, when your partner paid €74.10 of €100k. The partner owns 0.0741% of the Market Value upon exit.
- In Feb 2022, the principal portion is $314.60 of €423.85 (i.e. 74.22%). Therefore, when your partner paid €74.22 of €100k. The partner owns additional 0.07422% of the Market Value upon exit, in total the partner now owns 0.14832% of the Market Value upon exit.
- Repeat calculation for each month until exit.
This method allows your partner to increase payment from €100 per month up to the whole mortgage monthly payment (i.e. €423.85 in this example). However, when the actual mortgage's time is up, the partner cannot pay you anymore.
Your model assumes that the property has linear pricing from the formation of partnership to dissolution.
This is not realistic.
For example, consider that you bought a property in 2000 for €100k. In 2007 it became €200k and your partner joined you. Then there was a financial crisis in 2008-2011 and by 2011 it became €150k. In your model, you would have made your partner "lost 25% money" because you assumed that the partner held from €200k to €150k. In reality, you bought it at €100k and "made 50% money" from 2000 to 2011. Taking into the fact that you charged your partner "-25%", you made even more than 50%, which is not fair.
A mortage is different from a Real Estate Investment Trust. You entered the housing market at the beginning, and neither you nor the partner "purchased" the property under a Dollar Cost Averaging.
On the other hand, if you bought the property literally decades ago e.g. 1950, should the great gains from 1950 to 2007 be shared with the partner? Probably not. In that case, the model should use a "step up" cost basis of the property as if you "re-mortgaged" the loan upon formation of the partnership, similar to your proposal but using amortization table instead of "linear interpolation of start and end market value".
- You bought the property in Jan 2012 for €100k (p.s. irrelevant) at 2% interest for 25 years with 0%
- By Jan 2022 the outstanding principal portion is €65866.14 (p.s. irrelevant) according to amortization table, but the market price of the property is €150000.
- You draw a contract of a loan (you as lender and partner as borrower) that has a monthly payment of 100 at 2% interest for 25 years. Using financial calculators, such monthly payment can afford a property of €23593. If the partner paid €100 for 25 years = 100 x 12 x 25 = €30000, the partner would have paid €23593 principal and €6407 interest (of which some will be passed to your bank if you still have actual mortage).
- Essentially, the partner entered the housing market by buying €23593 of €150000 of your property.
- Whenever the partner wants to exit, the partner owns 15.7287% of the Market Value, minus the outstanding principal of the €23593 loan. What the partner gets has nothing to do with "linear interpolation".
If the €100 monthly payment suddenly increased after a while, it is considered as "Early Repayment of Loan". The entitled ownership is still 15.7287% of the Market Value, minus the outstanding principal of the €23593 loan, otherwise, the partner could have said "I'm paying you additional €126407 as if I owned 100% of the property and the partner takes the guaranteed retrospective profit. Of course you can formally "re-mortgage" the loan with your partner.