How Loan Amortization Works: Payments, Interest and Extra Payments

The payment formula, why a 30-year loan pays mostly interest for two decades, why the last payment is a few dollars off, and why an extra $10,000 saves nearly six times more in year 2 than in year 21.

The Payment Formula

A fixed-rate installment loan, such as a mortgage, car loan or personal loan, is repaid in equal monthly payments that cover that month’s interest and pay down some of the balance. The payment that clears the loan exactly at the end of the term is

payment = P × r ÷ (1 − (1 + r)⁻ⁿ)

where P is the amount borrowed, r the yearly rate divided by 12 and n the number of payments. For $300,000 at 6.5% over 30 years, r = 0.065 ÷ 12 ≈ 0.0054167 and n = 360, which gives $1,896.2041, rounded to $1,896.20. At a 0% rate the formula breaks down (it divides by zero) and the payment is simply P ÷ n. Our Loan Calculator does this and the schedule below it.

Why Early Payments Are Mostly Interest

Each month the lender charges interest on what you still owe: balance × r. In the first month of that $300,000 loan that is $300,000 × 0.065 ÷ 12 = $1,625.00, so only $271.20 of the $1,896.20 payment reduces the balance. As the balance falls, the interest share falls with it, which is the pattern the Consumer Financial Protection Bureau describes for mortgages and auto loans. The schedule shows how slow the start is:

Why the Last Payment Is Different

The exact payment, $1,896.2041, is rounded down to $1,896.20. That leaves about 0.4 cents a month unpaid, and because each shortfall itself earns interest, it grows to $4.71 by the end: the 360th payment is $1,900.91. Lenders handle this the same way, by adjusting the final payment, or by rounding the regular payment up so the last one is smaller. Either way the difference is a few dollars, not a sign of a mistake.

Extra Payments: Earlier Is Worth More

Money paid on top of the scheduled payment goes to principal, so every later month’s interest is charged on a smaller balance. Because interest is front-loaded, the same extra dollar saves far more early in the loan. We put a one-time $10,000 extra payment into the same $300,000 loan at three points:

A steady $200 a month from the start ends the loan after 277 payments and saves $103,450.19. Before paying extra, check that your lender applies it to principal rather than to next month’s payment, and that the loan has no prepayment penalty.

Term and Rate

A shorter term raises the payment but cuts the interest sharply: $300,000 at 6.5% is $2,613.32 a month over 15 years with $170,398.28 of interest, against $382,636.71 over 30. The rate matters as much: at 5.5% the 30-year payment is $1,703.37, at 7.5% it is $2,097.64. Use the interest rate on the note to work out the payment; the APR adds fees such as origination charges, so it is the figure for comparing lenders, not for the payment itself.

Mortgages: Taxes, Insurance and PMI

A house payment usually also collects property tax and homeowners insurance, and, on a conventional loan with less than 20% down, private mortgage insurance. Under the Homeowners Protection Act, as the CFPB explains it, PMI generally ends automatically when the balance is scheduled to reach 78% of the home’s original value, and you can ask to cancel it once the balance reaches 80%. On a $350,000 home with 5% down at 6.875%, that is payment 140 on the original schedule; $300 a month of extra principal brings the 80% point forward to payment 74. Our Mortgage Calculator adds these costs and shows both dates.

How We Checked These Numbers

Every figure here comes from the calculators’ shared engine, which works in whole cents and charges each month’s interest exactly. We compared it with an independent Python implementation using exact fractions on 2,007 random loans: all 305,948 schedule rows agreed to the cent. Your lender’s figures can still differ by small amounts if it charges interest by the day or the first period is not a full month.

Frequently Asked Questions

Published Oct 14, 2026 by Derek Giordano