How loan payments work: amortization explained

A fixed-rate loan is repaid in equal monthly payments, yet the amount you still owe falls slowly at first and quickly at the end. Knowing why helps you compare loan offers, judge whether a longer term is worth the lower payment, and understand what an extra repayment achieves. This guide explains the formula behind the payment and how to read an amortization schedule.

The payment formula

For a loan of principal P, a monthly interest rate r (the annual rate divided by 12), and n monthly payments, the fixed payment is:

payment = P × r ÷ (1 − (1 + r)^−n)

For 10,000 at 6% a year over 36 months, r = 0.005 and n = 36, which gives a payment of 304.22. Over the full term you pay 10,951.88, of which 951.88 is interest. At 0%, the formula reduces to principal divided by the number of months: 277.78 per month for the same loan, with a slightly smaller final payment to absorb rounding.

The loan payment calculator applies this formula, then builds the schedule month by month with interest rounded to cents, the way real statements work. The final payment is adjusted to clear the exact remaining balance, which is why it can differ by a few cents.

Reading an amortization schedule

Each month, interest is charged on the balance still outstanding, and whatever is left of the payment reduces the principal:

• Month 1: interest 10,000 × 0.5% = 50.00, principal 304.22 − 50.00 = 254.22, remaining balance 9,745.78.
• Month 2: interest 9,745.78 × 0.5% = 48.73, principal 255.49, remaining balance 9,490.29.
• Final month: interest is only about 1.51, so almost the whole payment goes to principal.

Early payments are interest-heavy because the balance is largest at the start. On long loans the effect is dramatic. On a 30-year mortgage, the first years of payments mostly cover interest, which is why the balance seems barely to move.

Longer terms cost more

Stretching a loan lowers the monthly payment but raises the total interest, often by far more than people expect. Borrowing 250,000 at 4.5%:

Interest rates matter just as much. The same 30-year loan at 6.5% instead of 4.5% costs 1,580.17 a month and 318,861.58 in interest, over 110,000 more for a two-point difference. Compare offers on total cost over the period you expect to keep the loan, not only on the monthly payment.

Nominal rate, APR, and what calculators leave out

The rate in the formula is a nominal annual rate divided by twelve. Lenders in many countries must also quote an APR (annual percentage rate) or an effective rate that includes fees and compounding, so two loans with the same nominal rate can have different APRs. Real schedules also depend on details a planning calculator cannot know: daily interest accrual, the actual payment dates, insurance or account fees, and payment holidays.

Use the calculator to compare scenarios and understand the shape of a loan, and use the lender’s official documents for exact figures.

What extra repayments do

An extra payment goes straight to principal, so every later month is charged interest on a smaller balance. Early in a loan, when the balance is highest, a modest overpayment can shorten the term by months and save a noticeable amount of interest. Before overpaying, check whether your loan charges early-repayment fees, and whether the lender shortens the term or lowers the payment. Both are common, and they have different effects.

Quick comparisons

1. Enter the principal, the nominal annual rate, and the term in months.
2. Note the monthly payment and the total interest.
3. Change one input at a time, such as the term or the rate, and compare.
4. Check the schedule to see how quickly the balance falls.

For the percentage side of these comparisons, such as how much more one offer costs in relative terms, the percentage calculator gives the percentage change between two totals.