Monthly payment
All loans are calculated with monthly payments of equal size. For an amount L, a monthly rate r and n months:
When the loan has a final balloon payment B (PCP, residual-value or deferred installment plans), its present value is taken off first:
Finding the rate from a payment
There is no simple formula for the rate when you know the payment, so the calculator searches for it. It tests rates between 0% and 100% a month, halving the range 200 times, until the payments (plus any balloon) are worth exactly the amount you received. That is accurate to far more decimal places than any lender shows.
Fees deducted from the loan are handled by lowering the amount received, which is how APR rules treat them.
Nominal and effective rates
- Nominal: monthly rate × 12. Used for the APR in the United States and Canada, the 実質年率 in Japan, and the rates quoted in South Korea, China, India and Nigeria.
- Effective: (1 + monthly rate)12 − 1. Used for the APR in the United Kingdom, the APRC across the EU (TAEG in France, effektiver Jahreszins in Germany), the CAT in Mexico and the CET in Brazil.
The calculator always shows both, so you can compare offers from different countries.
Flat rates
A flat rate charges interest on the original amount for the whole term:
The calculator then finds the reducing-balance rate that gives the same payment, using the search above.
Country-specific rules
- Mexico: 16% IVA is charged on interest, so the monthly rate used for the payment is the stated rate × 1.16. The CAT is calculated from the payments with IVA removed, as Banxico requires.
- Brazil: rates are entered per month. The CET is the effective annual rate including fees. The IOF estimate is 0.38% of the amount plus 0.0082% a day on each repayment of principal, counting at most 365 days.
- United Kingdom and EU: early repayment charges are capped at 1% of the amount repaid early (0.5% with 12 months or less left) and at the interest saved. In the UK no charge applies to £8,000 or less in 12 months, and in France to €10,000 or less.
- United Kingdom: the voluntary termination point is half the total amount payable.
Savings, depreciation and driving costs
- Savings: interest is credited monthly at (1 + yearly rate)1/12 − 1. Tax is taken on interest above any yearly allowance (Germany, UK), or as a yearly percentage of the balance in Mexico, where ISR is withheld on capital.
- Car value: the negative equity calculator reduces the value each month at the yearly rate you enter, compounded.
- Gig driving: fuel used is distance ÷ economy (or distance × litres per 100 km ÷ 100). UK miles per gallon use the imperial gallon of 4.54609 litres. Mileage deductions use the official rate where one exists (IRS in the US, HMRC in the UK, €0.30/km in Germany, the barème kilométrique in France) and actual costs elsewhere.
Where the rules come from
Country rules were checked in October 2026 against official sources, including the CFPB and IRS (United States), FCA, legislation.gov.uk and HMRC (United Kingdom), Canada’s Cost of Borrowing Regulations and Bank Act, German and French law, Banco Central do Brasil, Banxico, the Reserve Bank of India, the People’s Bank of China, and Korean and Japanese regulators. Each calculator lists the sources for the country you pick.
Example figures such as typical car prices, loan rates and fuel prices are estimates from market data and are labeled as examples.
Limits
Real loans can differ slightly: an odd first-payment date, daily interest, rounding, or add-ons can shift the numbers. Your lender’s disclosure is the official figure. Nothing here is financial, legal or tax advice.