How We Calculate: Car Finance Comparison

What This Calculator Does

The car finance comparison calculator answers “Which way of paying for a car costs the least?” by calculating the monthly payment, total cost, total interest, and true cost for four financing methods side by side: PCP, HP, Personal Loan, and Cash.

True Cost = Total Paid + Opportunity Cost. Opportunity cost is the investment returns you give up by spending money earlier. Cash purchase has the highest opportunity cost (all money spent on day one), while PCP has the lowest (smaller monthly payments leave more cash invested longer, and the balloon is deferred to the end).

Unlike single-type calculators, this tool lets you compare all options simultaneously with the same car price, deposit, and term — so the only variables are the APRs, PCP balloon percentage, and expected investment return.

The Two Payment Formulas

HP and Personal Loan (Standard Amortization)

Both HP and personal loans use the same formula — the standard amortizing loan:

Monthly Payment = PV × r × (1+r)^n / ((1+r)^n − 1)

Where PV = finance amount, r = monthly interest rate (APR/12), n = number of months. The loan is fully repaid by the end — no balloon or residual.

PCP (Balloon Payment Loan)

PCP uses a modified formula because a large balance (the balloon/GMFV) remains at the end:

Monthly Payment = r × (PV − FV/(1+r)^n) / (1 − (1+r)^−n)

Where FV = balloon amount. This produces lower monthly payments because you’re not paying off the full finance amount. But you’re paying interest on the full PV throughout the term, including the portion that becomes the balloon.

When APR is 0%, both formulas simplify to: Monthly = (PV − FV) / n for PCP, and Monthly = PV / n for HP/Loan.

How Each Variable Affects the Result

Car price scales everything proportionally. A £5,000 increase adds roughly £100–£120 to the monthly HP/Loan payment on a 48-month term at typical rates.

Deposit reduces the finance amount directly. Every £1,000 extra deposit saves roughly £20–£25/month on a 48-month term and reduces total interest by £100–£200.

Term length has opposite effects on monthly payment and total cost. Extending from 36 to 60 months drops the monthly payment by ~35% but increases total interest by ~60%. Shorter terms cost more per month but much less overall.

APR is the key differentiator between finance types. The gap between PCP (7.9%) and a personal loan (5.6%) on £22,500 over 48 months is £1,600+ in total interest. Always compare total interest, not just APR or monthly payment.

Balloon percentage (PCP only) determines how much of the car you’re actually paying off. A higher balloon means lower monthly payments but a bigger lump sum at the end — and more interest overall because the outstanding balance stays higher throughout.

Why True Cost Is What Matters

Monthly payment is what you feel in your budget each month. But true cost — total payments plus opportunity cost — is what you actually sacrifice for the car. Cash looks cheapest by total payments alone, but the opportunity cost of tying up all your capital on day one can be significant.

Example on a £25,000 car (£2,500 deposit, 48 months, 4.5% expected return):

• Cash: £25,000 total paid, but £4,920 opportunity cost → **£29,920 true cost**
• Personal Loan at 5.6%: £523/mo, ~£27,620 total, £2,850 opportunity cost → **£30,470 true cost**
• HP at 8.9%: £558/mo, ~£29,295 total, £3,010 opportunity cost → **£32,300 true cost**
• PCP at 7.9%: £370/mo, ~£30,280 total, £2,160 opportunity cost → **£32,440 true cost**

Cash wins here because the 4.5% return is lower than the loan APRs. But if your expected return exceeds the loan rate, financing and investing the difference becomes cheaper in true cost terms. The calculator lets you adjust the return rate to see exactly where the break-even point lies.

How Opportunity Cost Is Calculated

Each payment you make could have been invested instead. The opportunity cost of each payment depends on how long it had left to compound:

• Upfront payment (deposit/cash): grows for the full term → highest opportunity cost
• Monthly payments: earlier payments have more time to compound → decreasing opportunity cost
• Balloon payment (PCP): paid at the very end → zero opportunity cost

The closed-form formula avoids month-by-month loops:

Opportunity Cost = Upfront × ((1+r)^n − 1) + Monthly × (((1+r)^n − 1)/r − n)

Where r = monthly return rate (annual rate / 12), n = total months.

This is why PCP — despite having the highest total interest — can have the lowest opportunity cost: smaller monthly payments and a deferred balloon mean more of your money stays invested for longer.