What this calculator does
Compares Personal Contract Purchase (PCP) and Hire Purchase (HP) for the same vehicle. Takes car price, deposit, annual mileage, contract length, APR, and optional balloon/GMFV. Returns monthly payment for each, total cost of each, and equity position at end of term.
The formula
HP — standard amortising loan:
Principal = car price − deposit
Monthly payment = P × r / (1 − (1 + r)^−n)
Where r = APR / 12, n = term months
Total cost = deposit + (monthly × n)
PCP — balloon loan:
GMFV (Guaranteed Minimum Future Value) = estimated residual value
(set by lender; reflects expected depreciation and mileage)
Amount financed = car price − deposit − GMFV / (1 + r)^n
(GMFV is discounted to present value for amortisation purposes)
Monthly payment = Amount financed × r / (1 − (1 + r)^−n)
At end of term, three options:
1. Return the car (walk away)
2. Pay GMFV to own it
3. Use any equity (car value > GMFV) as deposit on next deal
Total cost if returning car = deposit + (monthly × n)
Total cost if buying outright = deposit + (monthly × n) + GMFV
Assumptions
- APR is flat and remains constant throughout the term.
- GMFV is provided by the user or estimated at 40% of car value for illustration.
- Mileage is used only for GMFV guidance, not as a direct input to the formula.
- No option-to-purchase fee is modelled separately (typically £100–200).
- No balloon refinancing is modelled.
Data sources
No regulatory rate data is used. FCA CP23/8 notes that approximately 80% of new cars are financed; typical new car PCP terms are 3–4 years. GMFV estimation is illustrative only — the real GMFV is set by the lender, not derived from a formula.
Limitations
- Real GMFV is set by the lender — the calculator accepts user input rather than computing it.
- Excess mileage charges are not modelled.
- Does not model GAP insurance or maintenance packages.
- Does not distinguish between FCA-regulated agreements and other finance types.
Worked example
Inputs: £20,000 car, £2,000 deposit, 48-month term, 8.9% APR, GMFV = £8,000 (PCP only).
HP:
Principal = £20,000 − £2,000 = £18,000
r = 8.9% / 12 = 0.741% = 0.00741
Monthly = £18,000 × 0.00741 / (1 − 1.00741^−48) = £447
Total cost = £2,000 + £447 × 48 = £23,456
PCP (GMFV = £8,000):
Amount financed = £18,000 − £8,000 / (1.00741^48)
= £18,000 − £5,593 = £12,407
Monthly = £12,407 × 0.00741 / (1 − 1.00741^−48) = £308
Total cost (return car) = £2,000 + £308 × 48 = £16,784
Total cost (buy) = £16,784 + £8,000 = £24,784
Changelog
| Date | Change |
|---|---|
| May 2026 | Initial publication |