How Mortgage Payments Are Calculated

The formula

M = P × r(1 + r)ⁿ ÷ ((1 + r)ⁿ − 1)

P is the loan amount, r is the monthly interest rate (annual rate ÷ 12), and n is the number of monthly payments (years × 12).

Why this exact shape

The formula answers: what fixed payment, made n times with interest accruing monthly on the remaining balance, brings the balance to exactly zero on the final payment?

It's the solution to a present-value equation — the lender is indifferent between $300,000 today and your stream of 360 equal payments, discounted at the loan rate.

Why early payments are mostly interest

Each month's interest charge is balance × monthly rate. On a new $300,000 loan at 6.5%, the first month's interest is about $1,625 — out of a $1,896 payment, only $271 reduces the balance.

By the final years the balance is small, so almost the whole payment is principal. The payment never changes; its composition flips completely.

What the formula leaves out

• Property taxes and homeowner's insurance (often escrowed into your real payment)
• Private mortgage insurance (PMI) when the down payment is under 20%
• HOA fees, and lender fees folded into the APR
• Rate changes — the formula assumes a fixed rate for the full term

Try the extremes

Set the term to 15 years in the calculator and watch total interest fall by more than half while the payment rises far less than double. Set the rate to 0% and the formula collapses to simple division: principal ÷ months. Both extremes are good sanity checks for any mortgage quote you receive.