True cost of a mortgage when considering inflation has an answer by a Chris Degnen with the relevant formula(s):
adjusted = (p - (1 + inf)^-n*p)/inf;
pv = Σ p2 (1 + r2)^-k for k = 1 to n
∴ pv = (p2 (1 + r2)^-1) + (p2 (1 + r2)^-2) + (p2 (1 + r2)^-3).
My first question is whether or not these are performing the same calculations. Unlike 'real interest' (which simply subtracts rate of inflation from rate of interest) this method is supposed to account for the effect of inflation on each payment on the amortization schedule, which to me seems like the right way to do it.
In my mind the inflation adjusted value of the 2nd month's payment should be derived by dividing the first month's payment by the monthly inflation rate (I'll come back to this). So if we had an arbitrary monthly installment of $100 we would divide that by a monthly inflation rate of say 1.05 (5%). We would then divide the product by 1.05 for the third month and so on.
If this is not what's happening in the above formulas please explain why this would not be the correct method. If this is indeed correct what I would really like is an in depth illustration of how the individual parts of the formula(s) are accomplishing what's playing out in my head. If that's going to be too verbose to post I'd appreciate some useful links instead.
As an aside is it convention to show annual inflation as a nominal rate as Chris does?
Nominal inflation = 5%; 5%\12 = 0.41666% monthly inflation; (1+0.0041666)^12 - 1 = 0.05116 = 5.116% for effective rate. If 5% is actually the effective rate then you'd need the 12th root of that to get the monthly rate. Or maybe they add every month's rate and divide by 12 (mean?), I don't know.