Formula for calculating the monthly payment for a Personal Contract Purchase

With

s = principal
n = no. periods
m = periodic payment
r = periodic rate
b = balloon

where the balloon is paid at the same time as the final payment in month n

The present value of the principal is equated to the net present values of the payments; then the summation is converted to a closed-form expression by induction.

∴ s = (m - m (1 + r)^-n)/r + b/(1 + r)^n

∴ m = (r ((1 + r)^n s - b))/((1 + r)^n - 1)

Assuming the dealer contribution is deducted from the initial amount.

s = 20000 - 2000 - 1000
b = 1000
r = (1 + 7/100)^(1/12) - 1
n = 36

∴ m = (r ((1 + r)^n s - b))/((1 + r)^n - 1) = 498.12

or calculating with APR as a nominal rate compounded monthly

s = 20000 - 2000 - 1000
b = 1000
r = 7/100/12
n = 36

∴ m = (r ((1 + r)^n s - b))/((1 + r)^n - 1) = 499.87

Looks like the website is using nominal rates. However, UK uses effective rates.