Amortization is the schedule that turns a loan into a sequence of equal payments. Each payment covers the month's interest first, and whatever remains reduces the principal. As the principal falls, the interest charged each month falls too, so a growing share of the same payment retires principal. That shifting split is the whole story of a mortgage.
The payment formula
The fixed monthly payment M on principal P at monthly rate r (annual rate ÷ 12) for n months is: M = P × r(1+r)ⁿ ÷ ((1+r)ⁿ − 1). It is calibrated so the balance lands exactly at zero after the last payment.
Month one, computed by hand
Take a $320,000 loan at 6.25% for 30 years. The monthly rate is 0.0052083 and n = 360. The formula gives a payment of $1,970.30. Month one: interest = 320,000 × 0.0052083 ≈ $1,666.67. Principal = 1,970.30 − 1,666.67 ≈ $303.63. Only about 15% of the first payment is your money coming back, the rest is the lender's charge for the largest balance you'll ever carry.
| Year | Principal (year) | Interest (year) | Balance at year-end |
|---|---|---|---|
| 1 | $3,865 | $19,779 | $316,135 |
| 5 | $4,952 | $18,691 | $298,901 |
| 15 | $9,829 | $13,815 | $232,858 |
| 29 | $32,632 | $1,392 | $8,935 |
Why extra payments work so well
Add $200/month to the loan above and it pays off in about 282 months instead of 360: roughly 6.5 years early, while saving around $99,000 of interest. Every extra dollar of principal never accrues interest again for the remaining term.
Try it yourself
The mortgage amortization calculator reproduces this schedule with cent-accurate arithmetic, supports extra payments, and lets you download the full schedule as CSV.