How to Calculate a Loan Payment, Step by Step

A fixed-rate loan payment is one of the more useful pieces of arithmetic an adult can carry around in their head. Once you know the formula and what each variable does, the numbers a bank quotes you stop being magic — you can sanity-check a mortgage offer in a minute, see why a longer term is rarely the bargain it appears to be, and understand why an extra hundred pounds in year one is worth far more than the same hundred pounds in year twenty. This guide walks through the standard amortisation formula step by step, applies it to a realistic example, and then looks at the behaviour that falls out of it.

The formula

For a fixed-rate, fully amortising loan — meaning the rate does not change and the loan is paid off in full by the end of the term — the monthly payment is given by:

M = P × [ r(1 + r)^n ] / [ (1 + r)^n − 1 ]

The four variables are:

• M — the monthly payment, which is what you are solving for.
• P — the principal, meaning the amount you actually borrow. Not the price of the house, not the price of the car — the amount the lender hands over after deposits, fees and so on.
• r — the monthly interest rate, expressed as a decimal. If the annual rate is 5%, then r = 0.05 / 12, which is roughly 0.004167.
• n — the total number of monthly payments. A 25-year loan paid monthly is 25 × 12 = 300 payments.

That is the entire model. Everything else — the schedule, the total interest, the impact of overpayments — is a consequence of this one line.

A worked example: £200,000 over 25 years at 5%

Take a typical UK mortgage: a principal of £200,000, an annual rate of 5%, and a term of 25 years. The variables resolve to:

• P = 200,000
• r = 0.05 / 12 ≈ 0.0041667
• n = 25 × 12 = 300

The expression (1 + r)n evaluates to about 3.4813. Plugging everything in:

M = 200,000 × [ 0.0041667 × 3.4813 ] / [ 3.4813 − 1 ]
M = 200,000 × [ 0.014506 ] / [ 2.4813 ]
M ≈ 200,000 × 0.005846
M ≈ £1,169.18

So the monthly payment lands at roughly £1,169. Over 300 months that is about £350,754 paid in total, of which £150,754 is interest. You can confirm this and play with the inputs in the Mortgage Calculator or the more general Loan Calculator.

Why the first payments are almost all interest

Here is the part that surprises people. The monthly payment is fixed, but the split between interest and principal is not. Each month, the lender charges interest on the outstanding balance for that month. In month one, the balance is the full £200,000, so the interest portion of that first payment is:

Interest_1 = 200,000 × 0.0041667 ≈ £833.33

The payment is £1,169.18, so the principal portion is whatever is left: about £335.85. After that first payment, the balance drops to roughly £199,664. The next month's interest is calculated on that smaller balance, so it is a tiny bit less, and the principal portion is correspondingly a tiny bit more. Each month the balance shrinks, the interest charged shrinks, and the share of the payment going to principal grows.

Early on, that shift is glacial. By the midpoint of a 25-year mortgage you have paid off only about a third of the principal, despite having made half the payments. The curve only really tips in your favour in the last third of the term, when the balance is small enough that interest is no longer eating most of each payment.

What an amortisation schedule looks like

An amortisation schedule is just a table that walks through every payment, showing how each one is split. To keep the numbers readable, here is a small example: a $10,000 loan at 6% annual interest over 24 months. The monthly payment works out to about $443.21.

The pattern is the same at every scale. The first payment is 89% principal here only because the loan is small and short; on a 25-year mortgage the first payment is closer to 30% principal and 70% interest. The final payment, by contrast, is almost entirely principal — the balance is so small that the interest charge has nowhere to land.

Term length and the interest balloon

The single biggest lever on total interest is the term. A longer term gives you a lower monthly payment, which is appealing, but the cost compounds month after month and the totals get uncomfortable. Holding the £200,000 principal and 5% rate constant, the same loan looks like this at three common terms:

Stretching the term from 15 to 30 years cuts the monthly payment by about a third, but more than doubles the total interest paid. The extra 15 years are mostly funding interest, not building equity. That is not an argument that the shorter term is always right — affordability and flexibility matter — but it is worth seeing the trade in numbers rather than abstractly.

Why early overpayments are disproportionately powerful

Because interest each month is charged on the outstanding balance, any principal you knock off early avoids interest on every subsequent month. An extra £1,000 paid in month one of a 25-year mortgage at 5% does not just save you £1,000 — it saves the compounding interest that £1,000 would have attracted across the remaining 299 months, which works out to roughly £2,400 of avoided interest and several months shaved off the term.

The same £1,000 paid in year twenty saves only the interest for the remaining few years, which is a much smaller number. This is why financial advisers often suggest directing windfalls — bonuses, tax refunds, inheritances — at mortgage principal in the early years rather than the later ones, assuming there is no penalty for overpayment. Always check your loan's terms; some fixed-rate products cap how much you can overpay each year without a fee.

The same maths, working in your favour

The reason a loan feels so heavy in the early years is the same reason a savings account feels so light in the early years: compound interest is patient. Money invested at a steady rate of return grows by a small amount each period, but each period's growth is calculated on a slightly larger base, and over decades that produces curves that look almost flat at first and then tilt sharply upward.

£5,000 invested at a 6% annual return becomes about £5,300 after one year — unimpressive — but about £16,000 after twenty years and £28,700 after thirty, without adding another penny. The Compound Interest Calculator is useful for seeing how the curve behaves with regular contributions layered on top, which is where most real savings plans live.

Fixed-rate versus variable-rate

The formula above assumes a fixed rate — r is the same every month for the life of the loan. Variable-rate and tracker mortgages reset the rate periodically, often against a central bank base rate, which means the payment recalculates whenever the rate moves. The arithmetic at any given moment is the same, but the payment, term, and total interest all become moving targets. This guide focuses on fixed-rate loans because they are the cleaner mental model; if you are on a variable product, treat any projection as a snapshot, not a promise.

APR versus nominal rate

The headline interest rate a lender quotes is the nominal rate. The APR (annual percentage rate) is the nominal rate plus the effect of mandatory fees and charges, expressed as a single annualised figure so that loans with different fee structures can be compared on a like-for- like basis. If two lenders both quote 5% but one has £2,000 of arrangement fees and the other has none, their APRs will differ even though the nominal rates match. When shopping around, compare APRs, not headline rates.

A note on what this guide is not

This is an explanation of the maths, not financial advice. Real mortgage and loan decisions involve tax treatment, product features, early-repayment charges, affordability assessments, and personal circumstances that no formula captures. For a decision of that size, speak to a qualified mortgage broker or independent financial adviser regulated in your jurisdiction. Use the Loan Calculator and Mortgage Calculator for modelling and comparison; use a professional for the contract.

The short version

A fixed-rate loan payment is determined by three inputs — principal, rate, and term — fed through one formula. The interest portion of each payment is largest at the start because it is calculated on the outstanding balance, which is highest at the start. Longer terms drop the monthly payment but multiply the total interest, sometimes by an order of magnitude over a working lifetime. Early overpayments save disproportionate amounts because they avoid interest on every payment that follows. And the same compounding that makes early-stage debt feel relentless makes early-stage saving feel quietly powerful, given enough time.