Fair Value of a monthly payment given two Bank Payment structures
There is one basic principle to apply here:  to compare money paid at different times, all the amounts must be compounded or discounted to the same point in time. In this case, the moment of the initial  $225,000 loan is convenient. At that moment, you get $225,000 You then make 30 payments on the 40% mortgage.  The amount of these payments has to be calculated;  they're paying off a $90,000 mortgage with 30 monthly payments at a monthly rate of 0.5% Finally, you make 30 payments of an amount X, starting one month after the 40% mortgage ends. So far we've just listed the amount and time of all the payments back and forth. A time-line type diagram is a huge help here. Finally, use compound interest and annuity formulas to bring all the payments to the starting point, using an interest rate of 1% a month! Equate money in with money out and solve for X
Varying the amount to reflect income during the quarter is entirely legitimate -- consider someone like a salesman whose income is partly driven by commissions, and who therefore can't predict the total. The payments are quarterly precisely so you can base them on actual results. Having said that,  I suspect that as long as you show Good Intent they won't quibble if your estimate is off by a few percent. And they'll never complain if you overpay. So it may not be worth the effort to change the payment amount for that last quarter unless the income is very different. You can choose to pay your mortgage instead of another bill, or vice versa.  Your net will change from month to month while your gross is relatively static. I can make a bunch of promises to my load officer about my expenses, but it is very difficult to verify.  Moreover, it is pretty hard to give your net income and plan for emergencies. So for the sake of reliability, verifiability, and general ease a lender will look at your gross. YOU should definitely look at your net when deciding if you can afford a loan. Inflation is not applicable in the said example. You are better off paying 300 every month as the balance when invested will return you income. "The Solicitor involved up front should be able to place constrictions as your suggesting.  I think you should look carefully at the desired wording. You deserve a return on your £100k. Say, the day after you buy (this is hypothetical, please bear with me) a developer says he needs the property and will give you £460k. Your wording here says you get £100k, and then, after the mortgage split £230k, but it seems more reasonable that your deposit doubles to £200k, the remaining £260k pays the mortgage, and the £130k left is split, £65k each.  My method accounts for the value of your £100k. Some would ask, why not apply the mortgage rate to that deposit? Because the home value may grow at a different rate. In my opinion, it's fair to apply the home value growth to the £100k deposit.  ""Fair"" means different things to different people. This is my opinion, and a suggestion. Consider it, and do what you and your partner wish. Use a solicitor. Put it in writing." Yes that is the case for the public company approach, but I was referring to the transaction approach:   Firm A and Firm B both have $100 in EBITDA. Firm A has $50 in cash, Firm B has $100 in cash.  Firm A sells for $500, Firm B sells for $600.  If we didn't subtract cash before calculating the multiple: Firm A: 5x Firm B: 6x  If we DO subtract cash before calculating the multiple: Firm A: 4.5x Firm B: 5x  So yea, subtracting cash does skew the multiple. Typically, this is not an option, as the monthly payments are fixed. It depends on the willingness of your financing bank for such a change. You probably will have to refinance (with them or another lender); which is not a bad thing, as you even can get a lower interest rate potentially (as of Jan 2017 - this will change). Consider too: It could be a better solution to instead invest the 25000, and use the investment returns to fill up the difference every month. Certainly more effort, but you probably come out ahead financially. "Your thinking is unfortunately incorrect; an amortising loan (as opposed to interest only loans) pay down, or amortise, the principal with each payment. This means that the amount that is owed at prepayment will always be less than the total borrowed, and is also why some providers make a charge for prepayment. The ""fairness"" arguments that you make predicated on that misunderstanding are, therefore, incorrect." You need the Present Value, not Future Value formula for this. The loan amount or 1000 is paid/received now (not in the future). The formula is $ PMT = PV (r/n)(1+r/n)^{nt} / [(1+r/n)^{nt} - 1] $  See for example http://www.calculatorsoup.com/calculators/financial/loan-calculator.php With PV = 1000, r=0.07, n=12, t=3 we get PMT = 30.877 per month As BrenBarn points out in his comment, the real values are inflation adjusted values using the consumer price index (CPI) included in the spreadsheet.  The nominal value adjusted by the CPI gives the real value in terms of today's dollars. For example, the CPI for the first month (Jan 1871) is given as 12.46 while the most recent month (Aug 2016) has a reported CPI of 240.45. Thus, the real price (in today's dollars) for the 4.44 S&P index level at Jan 1871 is calculated as 4.44 x 240.45 / 12.46 = 85.68 (actually reported as 85.65 due to rounding of the reported CPIs).  And similarly for the other real values reported. The calculation can be made on the basis that the loan is equal to the sum of the repayments discounted to present value.  (For more information see Calculating the Present Value of an Ordinary Annuity.) With Deriving the loan formula from the simple discount summation.  As you can see, this is the same as the loan formula given here. In the UK and Europe APR is usually quoted as the effective interest rate while in the US it is quoted as a nominal rate.  (Also, in the US the effective APR is usually called the annual percentage yield, APY, not APR.) Using the effective interest rate finds the expected answer. The total repayment is £30.78 * n = £1108.08 Using a nominal interest rate does not give the expected answer. "Taking the last case first, this works out exactly. (Note the Bank of England interest rate has nothing to do with the calculation.) The standard loan formula for an ordinary annuity can be used (as described by BobbyScon), but the periodic interest rate has to be calculated from an effective APR, not a nominal rate.  For details, see APR in the EU and UK, where the definition is only valid for effective APR, as shown below. 2003 BMW 325i £7477 TYPICAL APR 12.9% 60 monthly payments £167.05 How does this work? See the section Calculating the Present Value of an Ordinary Annuity.  The payment formula is derived from the sum of the payments, each discounted to present value. I.e. The example relates to the EU APR definition like so.  Next, the second case doesn't make much sense (unless there is a downpayment). 2004 HONDA CIVIC 1.6 i-VTEC SE 5 door Hatchback £6,999 £113.15 per month ""At APR 9.9% [as quoted in advert], 58 monthly payments"" 58 monthly payments at 9.9% only amount to £5248.75 which is £1750.25 less than the price of the car. Finally, the first case is approximate. 2005 TOYOTA COROLLA 1.4 VVTi 5 door hatchback £7195 From £38 per week ""16.1% APR typical, a 60 month payment, 260 weekly payments"" A weekly payment of £38 would imply an APR of 14.3%." If I is the initial deposit, P the periodic deposit, r the rent per period, n the number of periods, and F the final value, than we can combine two formulas into one to get the following answer: F = I*(1+r)n + P*[(1+r)n-1]/r In this case, you get V = 1000*(1.05)20 + 100*[(1.05)20-1]/0.05 = 5959.89 USD. Note that the actual final value may be lower because of rounding errors. EDIT: After reading one of the comments on the original question, I realized that there is a much more intuitive way to think about this. If you look at it as a standard PV calculation and hold each of the cashflows constant. Really what's happening is that because of inflation the discount rate isn't the full value of the interest rate. Really the discount rate is only the portion of the interest rate above the inflation rate. Hence in the standard perpetuity PV equation PV = A / r r becomes the interest rate less the inflation rate which gives you PV = A / (i - g). That seems like a much better way to get to the answer than all the machinations I was originally trying. Original Answer: I think I finally figured this out. The general term for this type of system in which the payments increase over time is a gradient series annuity. In this specific example since the payment is increasing by a percentage each period (not a constant rate) this would be considered a geometric gradient series. According to this link the formula for the present value of a geometric gradient series of payments is: Where P is the present value of this series of cashflows.   A_1 is the initial payment for period 1 (i.e. the amount you want to withdraw adjusted for inflation).   g is the gradient or growth rate of the periodic payment (in this case this is the inflation rate)   i is the interest rate   n is the number of payments This is almost exactly what I was looking for in my original question. The only problem is this is for a fixed amount of time (i.e. n periods). In order to figure out the formula for a perpetuity we need to find the limit of the right side of this equation as the number of periods (n) approaches infinity. Luckily in this equation n is already well isolated to a single term: (1 + g)^n/(1 + i)^-n}. And since we know that the interest rate, i, has to be greater than the inflation rate, g, the limit of that factor is 0. So after replacing that term with 0 our equation simplifies to the following: Note: I don't do this stuff for a living and honestly don't have a fantastic finance IQ. It's been a while since I've done any calculus or even this much algebra so I may have made an error in the math. There is nothing fair / unfair in such deals. It is an art than a science.  what kind of things should be considered, to work out what would be a fair percentage stake A true fair value is; take the current valuation of the company [This can be difficult if it is small and does not maintain proper records]. Divide by number of shares, that is the value of share and you should 20K worth of such shares. But then there is risk premium. You are taking a risk that an small start-up may do exceedingly well ... or it may close off. This risk premium is what is negotiated. It depends on how desperate the owner of the small company is; who all are interested in this specific deal ... if you want 30% share; someone else is ready to offer 20K for 15% of share. Or there is no one willing to lend 20K as they don't believe it will make money ... and the owner is desperate, you may even get 50%. I don't understand the logic of converting a cost of funds of 4% to a monthly % and then subtracting that number from an annual one (the 1.5%).  Unfortunately without seeing the case I really can't help you...there was likely much you have left out from above.