I published the math behind the CUMIPMT() & CUMPRINC() functions at the bottom of my spreadsheet for the post Annuity – Excel Functions and Math. I think it got lost in all the annuity math. When I Google the math for these two functions, my blog doesn’t show up until the 6th or 7th page, depending on the wording of the search. I see the question asked without a real answer, so I am posting the formulas again by themselves. I am also doing it because it is my blog and I can.
Also the math for a single row of a simple amortization schedule: