Car finance calculator

How are PCP and hire purchase payments calculated?

Both start with the credit: the car price less the deposit. A £25,000 car with £2,500 down leaves £22,500 to finance. Interest is charged monthly at the rate that compounds to the APR over a year: at 8.9% APR that is (1.089)^(1/12) - 1 = 0.71303% a month.

• Hire purchase repays the whole £22,500 in equal monthly payments: L x i / (1 - (1 + i)^-n). Over 48 months that is £555.19 a month, and the car is yours after the last payment.
• PCP, personal contract purchase, sets part of the credit aside as an optional final payment, here £9,000. The monthly payments repay the rest plus interest on everything: (L - B x (1 + i)^-n) x i / (1 - (1 + i)^-n) = £397.28 a month. At the end you can pay the £9,000 and keep the car, or hand it back under the agreement's conditions.

On PCP the balance falls much more slowly: after 2 years £16,324.11 is still owed, against £12,206.86 on hire purchase. The chart beside the result draws both balances month by month.

PCP or hire purchase: how do the costs compare for the same car?

With the same £25,000 car, £2,500 deposit, 8.9% APR and 48 monthly payments:

PCP is £157.90 a month cheaper, but if you pay the final payment to keep the car it costs £1,420.72 more overall, because the £9,000 stays borrowed, and charged interest, for all four years. If you hand the car back instead, you will have paid £21,569.63 for four years' use and own nothing. Which suits you depends on whether you want the car at the end; the calculator shows the arithmetic of both.

How does the optional final payment change a PCP?

A larger final payment lowers the monthly payment and raises the total, because more of the credit is carried to the end:

Moving the final payment from £5,000 to £13,000 cuts the monthly payment by £140.36 and adds £1,262.86 to the total. It also pushes back the month in which your payments reach half the total, which is the figure the next section turns on. The APR matters as well: at 5.9% the default PCP is £358.58 a month and at 11.9% £435.58, a gap of £77.01, while the hire purchase payments are £525.80 and £584.77.

What is voluntary termination, and how is half the total worked out?

Section 99 of the Consumer Credit Act 1974, as published on legislation.gov.uk, lets the debtor under a regulated hire-purchase or conditional sale agreement end it by giving notice, at any time before the final payment falls due. Section 100(1) sets what is owed: the amount, if any, by which one-half of the total price exceeds the sums paid and due, unless the agreement asks for less. Section 189 defines the total price as the total sum payable under the agreement, including any sum payable on exercise of an option to purchase. Arrears already due stay owed under section 99(2), and section 100(4) adds compensation if you have not taken reasonable care of the car.

Your agreement says whether it is a regulated hire-purchase agreement. Where a PCP is one, its total price includes the optional final payment, so the half-way point includes half of it. On the default figures:

• PCP: half of £30,569.63 is £15,284.81. After 24 payments you have paid £12,034.81, deposit included, so the top-up is £3,250. Without a top-up, the deposit and monthly payments reach half after payment 33 of 48.
• Hire purchase: half of £29,148.91 is £14,574.45. After 24 payments £15,824.45 has been paid, so no top-up is due; half is reached after payment 22.

A pattern in the PCP figure: exactly half-way through the term, the top-up is half the gap between the final payment and the deposit, (£9,000 - £2,500) / 2 = £3,250. The calculator counts the deposit as paid under the agreement; if your agreement states a different total amount payable, use its figure. A court can order a smaller sum where it covers the lender's loss, under section 100(3).

Why does the calculator not divide the APR by 12?

Under the FCA's consumer credit rules, CONC App 1.2.6R, a UK APR equates the present values of what is lent and what is repaid on an annual basis, which makes it an annual effective rate. The monthly rate that compounds to 8.9% over a year is 0.71303%, not 8.9% / 12 = 0.74167%.

Dividing by 12 overstates the payment: it gives £402.06 a month on the default PCP, £4.77 too high, and £558.85 on hire purchase. The difference grows with the APR. The calculator's figures are exact when the APR covers interest only; if the agreement includes fees, such as an option-to-purchase fee, its APR already reflects them and the monthly payment on the quote is the figure to trust. A US-style APR is worked differently, which the APR calculator sets out side by side.

Worked example in euros

The same arithmetic works in any currency, and nothing is converted. Take a €30,000 car with a €3,000 deposit at 6.9% APR over 36 months, and a €12,000 optional final payment:

1. Monthly rate: (1.069)^(1/12) - 1 = 0.55758%.
2. PCP payment: on €27,000 of credit with €12,000 deferred, €527.95 a month, €34,006.18 in total.
3. Hire purchase payment: €829.87 a month, €32,875.38 in total.
4. Half-way: after 18 payments the PCP top-up to half its total is (€12,000 - €3,000) / 2 = €4,500.

PCP saves €301.92 a month and costs €1,130.80 more in total if you keep the car. The UK Act does not govern an agreement made in euros elsewhere; the euro figures show only the arithmetic.

How do you calculate PCP payments in Excel?

Excel's PMT function takes a future value, which is exactly what a PCP final payment is. Microsoft documents the syntax as PMT(rate, nper, pv, [fv], [type]). Its fv argument is the balance to be left after the last payment, and a type of 0 puts each payment at the end of its period.

• PCP: =PMT((1+8.9%)^(1/12)-1, 48, -22500, 9000) returns 397.28.
• Hire purchase: =PMT((1+8.9%)^(1/12)-1, 48, -22500) returns 555.19.
• Half the PCP total: =(2500 + 48*397.28 + 9000)/2 returns about 15,284.72; with the unrounded payment it is £15,284.81.

This puts the final payment at the same date as the last monthly payment. Some agreements set it a month later, which changes the monthly figure a little.

Common mistakes and what this calculator leaves out

• Comparing PCP and hire purchase on the monthly payment alone. On the default car PCP is £157.90 a month cheaper and £1,420.72 dearer overall if you keep the car.
• Dividing a UK APR by 12. It is an annual effective rate.
• Leaving the final payment out of half the total. On a PCP that is a regulated hire-purchase agreement, the option payment counts.
• Forgetting arrears. Ending the agreement does not cancel payments already due.

The calculator does not model mileage limits and excess-mileage charges, the car's condition at return, option-to-purchase or admin fees, part-exchange with money still owed on the old car, insurance products, or the trade-in value of the car at the end. It does not decide whether your agreement is regulated or which kind it is. For a US-style car loan with sales tax and a trade-in, see the auto loan calculator.

Glossary

PCP: personal contract purchase, finance with lower monthly payments and an optional final payment to own the car. Hire purchase (HP): finance repaid in equal monthly payments, after which the car is yours. Optional final payment: the sum due at the end of a PCP if you keep the car, sometimes called the balloon. GMFV: the minimum future value a lender sets for the car at the end of a PCP, a figure some agreements tie to the final payment. Total amount payable: deposit, monthly payments and any final payment together. Total charge for credit: what the finance costs beyond the cash price. Voluntary termination: ending a regulated hire-purchase agreement early under section 99 of the Consumer Credit Act 1974.

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