Mortgage Payment

Standard amortizing payment, interest vs principal split, and remaining balance after k periods.

Name	Formula	Note
Periodic rate	`i = r / n` r annual nominal rate as a decimal; n payments per year.	r annual nominal rate as a decimal; n payments per year.
Payment (annuity)	`PMT = P × i(1+i)^N / ((1+i)^N − 1)` P principal, N = years × n. i ≠ 0.	P principal, N = years × n. i ≠ 0.
Interest portion	`interest_k = balance_{k−1} × i` Early periods are mostly interest.	Early periods are mostly interest.
Principal portion	`principal_k = PMT − interest_k` The rest of the payment reduces the balance.	The rest of the payment reduces the balance.
New balance	`balance_k = balance_{k−1} − principal_k` Ignores escrow, PMI, and fees unless added separately.	Ignores escrow, PMI, and fees unless added separately.

Open a calculator and put these formulas to work.