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How can I legally and efficiently help my girlfriend build equity by helping with a mortgage?
Have her pay something like a friendly monthly rent. This should be less than half of the monthly mortgage cost, since you are assuming the risk (and benefits) of a mortgage and closer to the rent of similar places near you. For when you get married and she is to have half the apartment, have a pre-agreed way to calculate a lump-sum that she needs to provide to match your own contributions up to that time, as if you two had equal contributions from the beginning. The financially precise way to do it would be to have her pay more than the mere sum of the amount (since she will be providing the amount at a later time than you), but I would be generous and skip this in your place if the difference is not too big. If you break up, she will have payed what would be a fair amount of rent, as if you two were renting, so, in this sense, it is fair that she would not have a claim on the apartment. In case that you two would like that she keeps the apartment, you can just sell it to her, having her pay this same amount as above and assume responsibility for the rest of the mortgage.