I think the formula is correct as it stands You can check it out on some test data eg loan of 1 million for 20 years 10 monthly Formula gives half life as 14 34 years near as d to 172 months and using Excel s PV function for the remainder 68 months we are a tad short of half way at 499401 52 With the minus sign in we get 5 66 years oh dear Derivation is from a continuous time mortgage model where the balance on a mortgage P t is given by the equation r interest rate T time period of loan and P0 is the original loan amount Once again this is something I have derived for myself but no doubt also once again there are more authoritative sources