Loan Amortisation: Where Each Payment Goes

A payment has two main jobs

On a standard amortising loan, each scheduled payment covers interest for the period and reduces principal. Interest is calculated from the outstanding balance under the loan's stated convention. The rest of the payment reduces what is owed. Because the balance changes over time, the split between interest and principal also changes even when the total payment remains level.

Early in a long fixed-rate loan, the balance is high, so the interest portion can be large. As principal is repaid, later interest charges are calculated on a smaller balance, allowing more of the same payment to reduce principal.

The fixed-payment formula

For a loan with principal P, periodic interest rate r, and n equal payments, the standard payment formula is P × r × (1+r)^n / ((1+r)^n - 1). If the rate is zero, the payment is simply principal divided by the number of payments.

That formula assumes a constant rate and equal payment intervals. Real products may use daily interest, different day-count conventions, fees, insurance, introductory periods, or variable rates. A calculator should therefore state what it includes rather than calling the output the exact lender payment in every case.

Why a longer term lowers the payment

Extending the term spreads principal repayment across more periods. That usually lowers the scheduled payment, but interest is charged for longer. If the rate and all other terms are unchanged, the lifetime interest bill is usually higher on the longer term.

This is why comparing loans only by monthly payment can be misleading. A lower payment can result from a lower rate, a longer term, a larger deposit, or some combination. Each mechanism has a different effect on total cost.

Extra payments change the schedule

An additional principal payment reduces the balance earlier than planned. Future interest is then calculated on a smaller amount, which can shorten the payoff time or reduce future required payments depending on the product's rules. The mathematical benefit depends on rate, timing, amount, and how the lender applies the payment.

Before assuming an overpayment works exactly like a calculator, check contractual limits, early-repayment charges, whether the payment is applied immediately to principal, and whether the lender recalculates the scheduled payment or term.

Interest rate changes break the original schedule

A variable-rate loan cannot be represented accurately by one fixed-rate amortisation schedule once the rate changes. At a reset, the lender may calculate a new payment based on the remaining balance, new rate, and remaining term. Stress testing therefore requires recalculating from the reset date, not simply adding the rate difference to the old monthly payment.

For comparison, model at least the current rate and one or more higher-rate cases. The purpose is sensitivity analysis, not a prediction that the higher rate will occur.

Fees belong outside the pure amortisation formula

Origination fees, closing costs, account fees, insurance, taxes, and penalties can make the real cost of borrowing differ from principal plus interest. APR or equivalent measures may help compare certain costs, but definitions vary by jurisdiction and product. A transparent model lists fees separately rather than forcing unrelated charges into the interest rate without explanation.

If a fee is financed into the loan, it increases principal and therefore may also generate interest. If paid upfront, it affects cash required at the start. Those are economically different even if the headline fee amount is identical.

Build an amortisation table

For each period, record opening balance, interest charge, payment, principal repaid, and closing balance. The closing balance becomes the next period's opening balance. This table lets you verify a calculator, examine the effect of extra payments, and identify exactly when a rate change or fee is applied.

Rounding can create small differences between a theoretical schedule and a lender statement. Financial institutions may calculate interest daily or round at different stages. For contractual figures, the lender's documents and statements are authoritative.

Authoritative references

Consumer Financial Protection Bureau: Mortgage key terms

Consumer Financial Protection Bureau: Loan Estimate explainer