How mortgage amortization works

On a U.S. fixed-rate mortgage the required principal-and-interest (P&I) payment is calculated once, at origination, and then stays the same. What changes every month is the split. The amortization schedule is the ledger of that split, payment by payment, until the balance is zero.

The monthly payment formula

Lenders use the standard level-payment formula. If P is the loan amount, r is the monthly interest rate (annual rate ÷ 12), and n is the number of months:

M = P × [r(1 + r)ⁿ] ÷ [(1 + r)ⁿ − 1]

At 0% interest the formula collapses to P ÷ n. AmortSheet rounds the quoted payment to the nearest cent, then applies interest each month as remaining balance × r, also rounded to cents — the same convention most U.S. servicers use on a simple-interest consumer mortgage.

Why the first payment is mostly interest

Interest is charged on whatever principal is still outstanding. On a $200,000 loan at 6%, the first month’s interest is about $1,000. The scheduled payment is about $1,199, so only $199 goes to principal. The next month, interest is calculated on $199,801. The interest slice shrinks by a few dollars; the principal slice grows by the same amount.

Late in the loan the picture reverses. The last payments are almost entirely principal because the balance — and therefore the interest — is small. That is why extra principal early in the term saves more interest than the same extra near the end: you remove dollars that would have been charged interest for decades.

How a schedule is built

1. Compute the fixed monthly P&I from principal, annual rate, and term.
2. For each due date, charge one month of interest on the current balance.
3. Apply the rest of the required payment to principal.
4. Apply any extra principal you designated for that month.
5. Carry the new balance forward. The last payment is whatever is still owed plus that month’s interest.

AmortSheet does not change the required payment when you prepay. That matches how most servicers treat a principal curtailment: the loan ends sooner; the bill does not automatically get smaller. A recast is a separate request.

What this model leaves out

• Property taxes, homeowners insurance, and mortgage insurance (escrow).
• HOA dues, origination fees, and discount points.
• Adjustable-rate resets, interest-only periods, and negative amortization.
• Daily simple interest on some HELOCs and a few portfolio loans.

If your draft is $400 higher than the P&I on this page, look at the escrow line on the statement before you assume the calculator is wrong.

Work the numbers yourself

Open the mortgage amortization calculator, leave the sample $350,000 / 6.5% / 30-year loan, and expand year one. Then add $200 extra monthly and compare the payoff date and total interest. The extra payments guide walks through when a lump sum beats a habit, and when it does not.