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How can I calculate the monthly payment for a PCP (Personal Contract Purchase) when given the variables below?

  1. 'Amount to be financed' - finance amount
  2. APR (annual percentage rate - %)
  3. Length of finance (duration)
  4. Final Payment (GMFV / balloon payment)

Need to get a formula to calculate this.

enter image description here

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6
  • Is there any way to calculate from APR? @ChrisDegnen
    – Agent 47
    Commented Oct 12, 2020 at 8:33
  • Could you please advise how to calculate monthly payment if balloon is not paid in monthly? carwow.co.uk/pcp-calculator I'm using this site to calculate. @ChrisDegnen
    – Agent 47
    Commented Oct 12, 2020 at 8:42
  • M = (R (B - L (1 + R)^N))/(1 - (1 + R)^N) This one, right? @ChrisDegnen Also, Here R=APR/12, Right?
    – Agent 47
    Commented Oct 12, 2020 at 8:53
  • For United Kingdom?
    – Agent 47
    Commented Oct 12, 2020 at 9:00
  • I've edited my question and added an image reference(Contains the values). @ChrisDegnen
    – Agent 47
    Commented Oct 12, 2020 at 9:07

1 Answer 1

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0 
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

eq

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.

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3
  • I think the following method is correct for my case. 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
    – Agent 47
    Commented Oct 12, 2020 at 9:36
  • r = (1 + 7/100)^(1/12) - 1
    – Agent 47
    Commented Oct 12, 2020 at 9:36
  • That is correct for the UK where APR is advertised as the effective rate.
    – Chris Degnen
    Commented Oct 12, 2020 at 9:37

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