Understanding auto EMI
One formula, four inputs, a monthly number.
The amortisation formula behind every car loan calculator, the dealer-finance trick to watch for, and the gap between APR and the actual monthly cost.
The EMI formula.
EMI (equated monthly instalment) is the fixed payment that pays off a loan in N months at interest rate r/12 per month. EMI = P · r/12 · (1+r/12)ⁿ / ((1+r/12)ⁿ − 1). Inputs: principal P (loan amount after down payment), annual rate r, term n (months). Same formula for mortgages and personal loans; the math is identical, the interest-rate range is different.
EMI = P · (r/12) / (1 − (1+r/12)⁻ⁿ)
A worked car loan.
A £30,000 car, £5,000 down payment, 5-year loan at 6.5 % APR. P = 25,000; r/12 = 0.005417; n = 60. EMI = 25,000 × 0.005417 / (1 − 1.005417⁻⁶⁰) ≈ £489/month. Total paid: £29,340 over 60 months. Interest paid: £29,340 − £25,000 = £4,340 — about 17 % on top of the borrowed amount.
£25,000 loan, 6.5 % APR, 60 months
EMI formula
Standard amortisation.
25000 × 0.005417 / (1 − 1.005417⁻⁶⁰) ≈ 489
= £489/month, £4,340 interest
APR vs the dealer's quoted rate.
Dealers often quote "5.9 % financing" without specifying APR. The legally-meaningful number is APR (annual percentage rate) which includes loan fees; the "interest rate" might exclude them. A 5.9 % rate with a £400 origination fee on a £25,000 loan is closer to 6.4 % APR. Always ask for the APR specifically; that's the one comparable across lenders.
Term length trades monthly for total.
Stretching a loan from 60 to 72 months drops the monthly payment but increases total interest. The same £25,000 at 6.5 % over 72 months: £420/ month (£69 cheaper) but £5,234 total interest (£894 more). 84-month auto loans now exist with 90-month outliers; financially these are mostly worse than buying less car. The monthly affordability is a real constraint; the term-length cost compounds against you.
The depreciation problem.
A new car loses 20-30 % of its value in the first year, 50-60 % by year five. Long-term loans on new cars routinely leave borrowers "upside down" — owing more on the loan than the car is worth — for 2-3 years. Selling or totalling the car during that window forces the borrower to pay the difference. The mitigation: bigger down payment (20 %+), shorter term, or buy used (depreciation already taken).
The cost of car ownership isn't just EMI.
Add insurance (£500-2000/year), fuel (£500-3000/year), maintenance (£300-1000/year), registration and tax (£100-500/year), parking. Total ownership cost is typically 50-100 % above the loan payment. The calculator gives you the EMI; build the rest into your budget before deciding what monthly is sustainable.