How Is Car Finance Calculated? The Formula Explained

The car finance payment formula

The monthly payment on a car loan or HP deal is worked out with the standard amortisation formula: M = P × [ r(1+r)^n ] ÷ [ (1+r)^n − 1 ]. P is the amount borrowed, r is the monthly interest rate (APR ÷ 12), and n is the number of monthly payments.

Every fixed-rate car finance quote, whether HP, a personal loan, or the monthly portion of a PCP, comes from that one formula. It calculates the level monthly payment that exactly pays off the principal plus interest over the term and leaves a zero balance at the end. Lenders use it, or an equivalent actuarial method, because it is the unique payment that amortises the loan smoothly.

Here is what each letter means. P, the principal, is the amount you actually borrow: the car's price minus the deposit, plus any fees rolled in. r is the monthly interest rate, which is the annual APR divided by 12. So a 9.9% APR gives r = 0.099 ÷ 12 = 0.00825. n is the number of monthly payments: 36, 48, 60, and so on.

The formula looks intimidating, but it only does two jobs. It compounds the interest month by month through the (1+r)^n term, and it spreads that total evenly across all n payments through the fraction. You do not have to work it out by hand; the main calculator does it instantly. But understanding the shape helps you see why the term and the APR matter so much.

Worked example: £10,000 at 9.9% APR over 48 months

Plug £10,000, a monthly rate of 0.00825 and 48 months into the formula and you get a monthly payment of about £253. Walk through it step by step and any quote becomes checkable.

Multiply that monthly by the term and you get the total amount payable: £253 × 48 ≈ £12,150, of which £10,000 is the principal and about £2,150 is interest. That is the whole calculation behind a 4-year quote. There are no hidden steps and no lender-specific magic. If a quote gives you a materially different monthly for the same P, r and n, then either the APR, the term, or an added fee is different from what you assumed.

The same walkthrough works for any amount. A £20,000 car with a £2,000 deposit, so P = £18,000, at 9.9% APR over 48 months gives M = £18,000 × 0.0253 ≈ £455. That is close to the £452 our HP calculator returns, and the small difference comes from day-count conventions and fee handling. Run the same numbers yourself on the main calculator and they will match.

1. Principal P = £10,000.
2. Monthly rate r = 9.9% ÷ 12 = 0.00825.
3. Number of payments n = 48.
4. Compound factor (1+r)^n = 1.00825^48 ≈ 1.4835.
5. Top of the fraction: r × (1+r)^n = 0.00825 × 1.4835 ≈ 0.01224.
6. Bottom of the fraction: (1+r)^n − 1 = 1.4835 − 1 = 0.4835.
7. Monthly M = £10,000 × (0.01224 ÷ 0.4835) ≈ £10,000 × 0.0253 ≈ £253.

Why interest is front-loaded

In the early months, almost every payment is interest on the full balance; only a sliver reduces the principal. That front-loading is why early settlement and overpayment save so much.

Each monthly payment splits into two parts: interest on that month's outstanding balance, and a reduction of the principal. At the start of the term the outstanding balance is at its highest, so the interest portion is at its highest too, often 70 to 80% of the payment in month one. As the principal is paid down, the interest portion shrinks and the principal portion grows, month by month, until the final payment is almost entirely principal.

On the £10,000 / 48-month / 9.9% example, month one's interest is about £82.50 (0.00825 × £10,000) out of the £253 payment, which means only about £170 clears the principal. By the final month the interest is under £5 and the rest clears the last of the balance. This is why a borrower who settles or overpays early can save a large share of the total interest: they remove principal that would otherwise have generated interest for many remaining months. Model it on the overpayment calculator.

Front-loading also explains negative equity. Because the principal falls slowly in the early years, a borrower two years into a long term still owes most of what they borrowed, while the car has depreciated fastest in those same years. The loan balance and the car value diverge, and the borrower is underwater. See the negative equity calculator for the mechanics.

How PCP is calculated differently

PCP uses the same amortisation formula, but the principal is the car's price minus the deposit AND minus the balloon (GMFV), so the monthly is lower and the balloon is paid separately at the end. Interest still accrues on the balloon throughout.

On PCP, the calculation splits the car's cost into two parts. The depreciation, which is price minus deposit minus balloon, you pay off monthly. The balloon (GMFV) you pay, hand back, or refinance at the end. The monthly payment is the amortisation formula applied to the depreciation amount only, which is why it comes out lower than HP on the same car.

The catch is that the balloon still accrues interest at the full APR for the whole term, even though you are not paying it down monthly. That interest is bundled into the monthly payment, which is why the total to own on PCP exceeds HP on the same car. On a £20,000 car with a £2,000 deposit and an £8,000 balloon at 9.9% APR over 48 months, the monthly is about £314 and the total to own is about £25,086. That is roughly £1,400 more than HP's £23,695, almost entirely because of the interest on the deferred balloon. Run it on the PCP calculator.

The balloon itself, the GMFV, is set up front by the lender, based on a prediction of the car's value at the end of the term given the agreed mileage. It is a forecast, not a market price, which is why, at the end of a PCP, the car can be worth more or less than the GMFV. If it is worth more, you have equity you can put toward a new deal. If it is worth less, you can hand it back and let the lender take the loss. That optionality is part of what you pay for via the higher total.

How the APR is calculated

The APR is the yearly cost of borrowing expressed as a percentage, including the interest rate and any compulsory fees, calculated so that the present value of all your payments equals the amount you borrow. It is the one number that lets you compare deals fairly.

APR is not simply the interest rate. It is derived by solving backwards. Given the schedule of payments, the monthly amount, the term, and any fees, what single annual rate makes the present value of those payments equal the principal? That rate is the APR. The FCA's CONC rules set out how it must be calculated, which is why APR is directly comparable between lenders. Two deals quoting 9.9% APR cost the same in percentage terms, even if one charges a fee and the other does not.

This matters because a low interest rate with a large fee can produce a higher APR than a slightly higher interest rate with no fee. The APR rolls both into one figure, so it is the number to compare, never the headline interest rate alone. Convert any APR into pounds of interest on the APR calculator, and read our flat rate to APR converter page to see why a low flat rate can hide a much higher APR.

One related point. The APR assumes you make every payment on time and hold the agreement to term. If you settle early, the statutory interest rebate under the Consumer Credit (Early Settlement) Regulations 2004 returns the unearned portion of that front-loaded interest, which is why early settlement on a long term can save so much. Work out your own rebate on the settlement calculator.

How settlement figures are calculated

An early settlement figure is the outstanding principal plus the interest accrued to the settlement date, minus a statutory rebate of the unearned (front-loaded) interest. The lender may add up to about one month's interest as a charge.

When you settle early, you do not pay all the remaining interest in the original schedule, because most of that interest was front-loaded into the later months you will no longer reach. The Consumer Credit (Early Settlement) Regulations 2004 give you a statutory right to a rebate of that unearned interest. So the settlement figure is the outstanding principal, plus interest accrued up to the settlement date, minus the rebate, plus any permitted lender charge, which is limited to roughly one month's interest and only applies in the early part of the term.

This is why settling early in a long term can save a large share of the total interest. The front-loaded schedule means a disproportionate amount of the remaining interest is rebated. The same logic applies to overpayments: each overpayment removes principal immediately, which shrinks every future interest charge. Model both on the settlement calculator and the overpayment calculator.