Mathematicians in here please

The other alternative here might be to reduce the size of the deposit so that both parties pay equal and then the party with the spare cash invests that money totally separately like a stocks and shares ISA. The interest rate is so low it's more likely that well invested money would rise better vs the low interest rate your paying on a mortgage.

If he's putting down 30% as a 75/25 split (as per the original post), then you'd be reducing your deposit from 30% to 15% to achieve that - I suspect that's not workable - a) to still be able to afford the house and b) to achieve decent LTVs on the mortgage even assuming you could afford it still
 
What sort of deposit difference are we talking about because that might make things clearer, also have you looked back at the examples to consider how long you have to stay in the property and how much of the outstanding mortgage you would have to pay back before a % split agreement becomes more favourable then a deposit return + 50/50 split after, because it can take quite a bit more then a few years, and relies heavily on a strong housing market on top of that as well.
Um, let's just say one deposit is more than 3x larger (to remain suitably vague). I'm taking on board what you've said here. Once I have a moment we're going to look at some examples (MSE's mortgage overpayment calculator is useful to see how much equity you've paid off/earned in XX years for example)

The other alternative here might be to reduce the size of the deposit so that both parties pay equal and then the party with the spare cash invests that money totally separately like a stocks and shares ISA. The interest rate is so low it's more likely that well invested money would rise better vs the low interest rate your paying on a mortgage.
What @Kenai said below. We are in London so the whole deposit is definitely needed to keep the mortgage affordable.
 
Um, let's just say one deposit is more than 3x larger (to remain suitably vague). I'm taking on board what you've said here. Once I have a moment we're going to look at some examples (MSE's mortgage overpayment calculator is useful to see how much equity you've paid off/earned in XX years for example)
Its more to understand the deposit as a % total of the overall purchase, you can provide that in % rather then a figure because then it makes feedback a little clearer.

Im tending towards @thenewoc advised %, and that in the event of any sale the derived % split must be on sale price not net proceeds of sale for you both to then get your share returns fairly on percentage.
 
All you need to do is determine the relative portion of the house that each party owns at the time it is sold. This will start at 75/25 the day you buy the house, and then as you make mortgage repayments it will start to slowly converge towards the 57.5/42.5 split described above.

I'll be honest, I can't be bothered to try and write out a universal formula for this, but if you get one of the standard mortgage spreadsheets that illustrates for a given interest rate, term etc how much money is owed on a property over time, you can use that as a starting point for figuring out how much each person owns, by plugging in the total amount each person has paid in relative to the net value of the property after the outstanding mortgage balance is repaid.

So perhaps you buy a house for £100k, you start off paying £22.5k and £7.5k respectivley. If you sell the house on day 1 for £110k the net value after repaying mortgage would be say 110-70 = £40k. One person gets £30k back, the other gets £10k back.

Then suppose over time each person has paid in another £10k and the outstanding mortgage balance is down to say £55k. You sell the property for £115k. You've now got a net balance of £60k. Person 1 has paid in £32.5k and person 2 has paid in £17.5k. So Person 1 takes 32.5/(32.5+17.5)*£60k = £39k, Person 2 takes 17.5/(32.5+17.5)*£60k = £21k.
 
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