# How is interest calculated on PCP agreements?

in December 2018, I'll be at the end of my PCP agreement for my current car and I'm weighing up my options. I've never really paid attention to the details about my previous finance agreements - I just knew I needed a car that wouldn't break down and signed the dotted line.

I was wondering if, given the information I know about my current agreement, if it's possible to calculate the interest I'm due over the duration of my PCP deal?

I've been trying to get do it on Google Sheets for a few days and although I get close, I can't quite match the figure I was given by the finance company. Even when I phoned the finance company for a breakdown, they told me I shout get a financial advisor.

If I use my real life figures as an example, I feel as if I should be able to calculate amount of interest I've been quoted to pay back but I can't - surely it's a science and they don't just pluck numbers out the air? :D

Car Price: £14,299
Deposit: £700
Credit Required: £13,599
Interest Rate: 3.5%
APR: 7.8%
Total Interest: £2,579.44

Repayment:

First Payment: £276.53 (includes £40 "Credit Facility Fee")
47 payments of: £236.53
Final Payment (GFMV): £4,825
Completion Fee: £299

I just can't figure out how, given the information above, the total interest is £2,579.44 and I'm worried it's been miscalculated?

Absolutely any information would be much appreciated, my finance company have been useless and I'm struggling to wrap my head around this.

• Does your contract say anything about including the £40 Credit Facility Fee and the £299 Completion Fee as part of the Credit Required, or have you paid it upfront and separately? Feb 19, 2018 at 15:25
• @theonlydanever my first payment was £276.53 which is the regular payment of £236.53 + the £40 facility fee. The completion fee is paid at the end along with the final payment, which takes that payment to £5,124 Feb 19, 2018 at 17:04

You might be finding it difficult to arrive at the exact number for a few reasons:

• they may be using a different interest frequency. For example, they could be working it out daily, monthly or yearly (even though you're paying monthly), but it will change the amount due.
• you only pay interest on the capital outstanding, so the amount of interest you pay will reduce over time. However, all your payments are equal - this is called amortisation. There are several amortisation methods, so you want to make sure you're using the same method as the credit supplier.

I can get within £5 of your £2,579.44 figure, but only when the £40 and £299 fees are included - I think the Credit Facility Fee and Completion Fee is where the problem lies. This article might give explain the APR a little better than I can (look at the sections on Multiple definitions of effective APR and Additional considerations) - it gives a little insight in to how even a small amount can massively affect the payment.

Also , just to give you some peace of mind - you're protected by the Financial Conduct Authority (FCA) in the UK and so, if the interest was found to be incorrect, even just a little bit, then they'd come down hard on the company you're leasing from... so there's a very, very good chance it's correct.

Hope this helps!

• thank you very much for your reply. I guess I take comfort in the fact there appears to be some "variable" aspect then so that explains why I can't quite calculate it! Feb 19, 2018 at 17:07
• Compounding frequency should not affect the interest or the amount due. As the link you included states: For Europe and the UK "A single method of calculating the APR was introduced in directive 98/7/EC", that being the effective interest rate. This is borne out by the equation in the link you provided, e.g. `(1 + APR/100)` etc. Nominal interest rates cannot be used in this manner. Feb 20, 2018 at 9:24
• @ChrisDegnen This article states that "The effect of compounding depends on the frequency interest is compounded". There's also this table on the link you posted (regarding effective interest rates) that shows the rate changing based on the compounding frequency? With all that said, OP is likely paying simple interest anyway, which is charged on a daily basis. Feb 20, 2018 at 10:18
• @theonlydanever The article you have quoted is appropriate for the US where they use nominal rates with specified compounding periods. By EU law the interest rate in the EU and UK is the effective interest rate. This does not depend upon the compounding period. The daily rate can be calculated from the effective rate. Clarifying the rate issue is quite important for this question and worthwhile settling. The best proof I know of is the equation in the EU section of the APR link which only works for an effective APR. Feb 20, 2018 at 11:58
• @theonlydanever You might find it interesting to look up loan calculators on US and UK sites. You will find the US sites calculate using the nominal rate method while the UK sites use the effective rate method. Feb 20, 2018 at 12:04

As theonlydanever mentions, you can get somewhere if you add the credit facility fee and the completion fee. However, I have had to add them to the balloon payment to reach the loan figure. This doesn’t account for the credit facility fee also being paid with the first payment. Also the completion fee is included in the loan and generates an interest charge.

Using the formula derived here: https://money.stackexchange.com/a/76041/11768

``````L = (B + (M ((1 + R)^N - 1)/R))/(1 + R)^N

where

L = present value of loan
M = periodic repayment
R = periodic rate
B = balloon payment
N = number of periods
``````

Taking the APR as the effective interest rate. (See note 1)

When

``````M = 236.53
R = (1 + 7.8/100)^(1/12) - 1 = 0.00628 (approx)
B = 4825 + 299 + 40 = 5164
N = 48

L = (B + (M ((1 + R)^N - 1)/R))/(1 + R)^N = 13599.38
``````

I don't know if this is the calculation your finance company is using, but it's odd how the figures come out.

The interest works out fairly simply using the following calculation

``````N M + 4825 - 13599 = 48*236.53 + 4825 - 13599 = 2579.44
``````

However, if the previous figures are used, with `B = 5164`

``````N M + B - L = 48*236.53 + 5164 - 13599.38 = 2918.06
``````

although this includes the closing fee.

The calculation can be illustrated like so, as the interest on the principal remaining month by month, up to the penultimate month. The principal remaining at month `n` is given by `P[n]`

``````P[n_] := (M + (1 + R)^n (R L - M))/R
``````

and the interest payable at the end of each month is `P[n] R`, e.g.

the first month's interest is `P R = 85.40` and the last is `P R = 33.70`.

The formula is derived here: https://money.stackexchange.com/a/73683/11768

Note 1 EU regulations specify APR is the effective annual rate, as defined in the above link. This is evident from the included equation: EU regulations also require that financial services providers provide a representative example, the basic figures for which have been provided. A more illustrative example would help since the figures don't seem to agree.