The maths behind the calculators

Last reviewed: September 2026

Loan payment calculation

All three calculators use the standard amortising loan formula. This is the same mathematics lenders use to build repayment schedules, and it is the correct model for any loan where each payment covers the interest accrued since the last payment plus a repayment of principal.

Where:

• M — the periodic payment (monthly, in our tools)
• P — the principal, meaning the amount actually borrowed
• r — the periodic interest rate, calculated as the annual rate divided by 12
• n — the total number of periods, calculated as the term in years multiplied by 12

When the annual rate is zero, the formula is undefined — division by zero. In that case the payment is simply the principal divided by the number of periods. Our calculators handle this case separately rather than returning an error.

Total interest and total cost

Total interest is the sum of every payment made over the life of the loan, minus the principal:

The personal loan calculator adds any origination fee to the principal before calculating, and reports the fee separately so you can see its effect on both the payment and the total cost. This matters: an origination fee raises your effective borrowing cost in a way that a headline interest rate does not show.

Payment schedule

For each period, the schedule is built in this order:

1. 1
   Interest for the period — the outstanding balance multiplied by the periodic rate.
2. 2
   Principal repaid — the payment minus that period's interest.
3. 3
   New balance — the previous balance minus the principal repaid.

Early in a loan, interest dominates and the balance falls slowly. Later, principal dominates. This is why paying extra early has a disproportionate effect on total interest, and why the payoff calculator allows extra payments to be applied at any point.

Debt payoff ordering

The debt payoff calculator compares two standard strategies across multiple balances:

Both strategies pay the minimum on every debt except the target, and direct all surplus at the target. When a balance is cleared, its payment rolls into the next target — this is the “rollover” that gives both methods their power.

The avalanche method always costs less in raw interest. The snowball method sometimes keeps people going long enough to finish. We present both with the numbers rather than recommending one, because which is better depends on you, not on the mathematics.

Currency handling

The calculators support multiple currencies and format results according to the selected currency's conventions. Conversions between currencies are not performed — if you borrow in one currency and earn in another, enter the figures in the currency of the loan and account for exchange-rate risk separately. No calculator on this site models exchange-rate movement, because that would require forecasting.

Indicative rates

Where a calculator pre-fills an interest rate, that figure is an indicative average for the selected currency, based on published national averages. It is a starting point, nothing more.

What these models do not do

A model that hides its limits is misleading. These are the things our calculators deliberately do not attempt:

• Variable rates. Monthly payments on a variable-rate loan change as the reference rate moves. We calculate on a fixed rate, because modelling future rate movements would mean forecasting them.
• Tax treatment. Interest deductions, tax treatment of forgiven debt, and similar rules vary by country and personal circumstance. None of it is modelled.
• Fees beyond origination. Late fees, insurance products bundled with a loan, prepayment penalties and currency conversion charges are not included unless you add them yourself.
• Credit decisions. No calculator predicts whether you will be approved, or on what terms.
• Inflation and opportunity cost. A pound repaid today is not the same as a pound repaid in ten years. Comparing a loan repayment against an investment return requires assumptions we are not willing to invent.

Accuracy and rounding

Calculations run at full floating-point precision. Values are rounded only for display, which means a total cost shown on screen can differ slightly from the sum of the rounded monthly figures shown alongside it. Where this happens, the total is the accurate one.

The final payment in a schedule is adjusted so the balance reaches exactly zero rather than leaving a residual fraction. This mirrors how real repayment schedules are constructed.

Verifying a result yourself

Every figure our calculators produce can be reproduced by hand using the formulas on this page. That is deliberate. If you get a different answer, one of two things is true: we have a bug, or an input differs — and we would like to know either way. Tell us and we will investigate.

Reference material

The banking directories follow a different method. Rather than calculating, they compile reference information from primary sources — deposit guarantee schemes, banking regulators and national authorities. That material is described in our editorial policy, including how often each type of content is reviewed.