Loan calculator

What is a loan calculator?

It answers the question a lender asks you to accept: if I borrow this much, at this rate, over this long, what do I pay each month? The arithmetic is the standard amortisation formula — each month, interest is charged on what you still owe, the payment covers that interest, and whatever is left over reduces the balance.

Because interest is charged on the falling balance, the split changes every month. Early on, most of the payment is interest; late on, most of it is principal. On a 30-year mortgage at 6.5%, the first payment is roughly four-fifths interest and the last is almost entirely principal, which is why the schedule is more informative than the single headline number.

This calculator works in whole cents throughout, because that is what money is, and it shows you the schedule it actually built rather than a formula's idealised output.

How to use the loan calculator

1. Enter the amount, rate and term. The rate is the nominal annual percentage, divided by twelve for each month — the ordinary way a loan is quoted. The term takes years or months, whichever you have.
2. Read the payment, and then the one below it. The monthly payment is the headline. The final payment sits directly under it, with the difference, because in almost every loan it is a different number.
3. Open the schedule if you want the detail. Every month is listed: what you pay, how much of it is interest, how much comes off the balance, and what is left. Copy takes the summary figures.

Your last payment is not the same as the others

The payment formula produces an amount with unlimited decimal places. Nobody can charge that, so it is rounded to the cent — and a rounded payment does not retire the principal exactly. After the second-to-last month there is a balance left that is not quite one payment, so the final payment is whatever remains plus that month's interest.

Measured over 3,000 randomly generated loans, from a thousand to eight hundred thousand, at rates from half a percent to twenty-five, over terms from one to thirty years, the final payment differs from the others in **98.5%** of them. Borrow 250,000 at 6.5% over 30 years and the monthly payment is 1,580.17 while the last one is 1,580.55. Borrow 500,000 at 3.1% over 25 years and the gap is 1.87. It goes the other way too: 30,000 at 7.9% over five years pays 606.86 a month and 606.64 at the end.

The gap is usually small change, but not always — on a large loan at a high rate it can run to hundreds. And it has a consequence beyond the final month, because it means the total interest that almost every calculator prints is wrong.

That figure is worked out as the payment times the number of months, minus the amount borrowed. Since the last payment is not the payment, the subtraction is off by exactly that difference. Every total on this page is summed from the schedule instead, so the numbers shown are the ones the schedule contains. The page shows what the multiplied-out figure would have claimed, so you can see the size of the discrepancy for your own loan.

Honest limitations

Rounding conventions vary between lenders, and this page uses one: interest is rounded to the nearest cent each month, and the level payment is rounded half up, which is what a spreadsheet's ROUND does. A lender that rounds the payment up instead will show a slightly smaller final payment; one that carries fractional cents internally will differ again. So treat the final-payment figure as the right shape and the right order of magnitude rather than a prediction of your lender's statement to the penny.

The month is treated as a twelfth of a year. Real lenders sometimes count actual days between payments, which makes February's interest smaller and a 31-day month's larger. That convention is not modelled here, and on a long loan it moves the numbers slightly.

Nothing but principal and interest is included. Arrangement fees, mortgage insurance, property taxes, payment protection and early-repayment charges all change what you actually pay and none of them are part of this calculation. A quoted APR usually folds some fees in, which is why an APR and a nominal rate are different numbers and why the payment here will not match a lender's APR-based illustration.

The rate is assumed fixed for the whole term. A tracker, a discount period or any variable-rate product will diverge from this schedule the moment the rate moves, and no calculator can tell you when that will be.

The engine is held to 44 assertions. The load-bearing one is not a table of expected answers but a closure property: over 1,200 randomly generated loans, every schedule must end at a balance of exactly zero and the monthly principal portions must sum to exactly the amount borrowed. A schedule that ends a penny out is one nobody would notice was wrong.

Why is it free?

It is arithmetic on three numbers, running in your browser as you type. Nothing about what you are borrowing is sent anywhere, which is worth stating plainly for a page that asks how much debt you are taking on.

There is no account, no cap on how many loans you compare, and nothing held back — the schedule is the useful part, so putting it behind a sign-up would defeat the point.