Lump Sum to the Liability Line, and the Cheaper Exit

How this is worked out

Which quantity the line is a share of

The agreement names a share you must have paid before you can hand the vehicle back. That share is measured against the total amount payable — everything the agreement would ever take, including the deposit, the fees, every monthly payment and the optional final payment at the end. It is not measured against the term, and it is not measured against the credit advanced.Almost everybody reads it as a share of the term, and on an agreement with a large final payment the two are a long way apart. The reason is the final payment itself: it is inside the total, the monthly schedule never collects it, and it is the payment you are terminating in order not to make.

The arithmetic

Write P for the amount of credit, r for the rate, n for the number of monthly payments, V for the optional final payment, D for the deposit, F for the fees, m for the payments made, h for the share you are liable for, q for the quoted settlement figure, S for the resale value and X for the charges on return:

A             = the level monthly payment on P at r over n, ending at V
B_m           = the balance outstanding after m payments

T             = D + F + n × A + V          the total amount payable
the line      = h × T
paid so far   = D + F + m × A
the lump sum  = max(0, h × T − paid so far)

terminate     = the lump sum + X
sell          = q − S
settle & keep = q                          (not ranked: a vehicle survives it)

The last three lines are the second half of the question and the part nothing else combines. Note what the middle one can be: where the vehicle is worth more than the settlement figure it isnegative, which is selling clearing the finance and leaving you with money rather than a cost at all.

Where the schedule comes from

A and B_m are not computed here. They are imported from the model this one extends — an amortising schedule with a non-zero terminal balance, which is exactly the capability that model added to its own parent — so the total amount payable this page prints and the balance it reads off are the same arithmetic and cannot drift apart. The verification behind this page asserts that by bit equality over a swept grid of agreements rather than by agreement to a tolerance, because a tolerance would pass for a close reproduction rather than for the parent’s own answer.

Why there is sometimes no month at all

The line is a share of a total that contains the optional final payment. The monthly schedule collects the deposit, the fees and n payments — and never that final payment. So where the share is large and the final payment is large,the line can sit above everything the monthly schedule will ever collect, and no payment number reaches it. That is not an edge case: it is the ordinary shape of an agreement with a large balloon, and it is the reason this page prints a sentence where a month would be rather than a month it does not have.

Why only two of the three routes are compared

Two of these end with you having no vehicle and one ends with you owning a car. Costs are only comparable when what you hold at the end of each is the same, soranking the settle-and-keep figure against the other two would set a cost against a cost less an asset, which is the comparison that makes the expensive route look like the cheap one. Every route is priced. Every route says whether a vehicle survives it. The cheaper-of is stated over the two for which one does not, and there is no arrangement of the figures on this page that produces a ranking of three.

What the settlement premium is, and what it is not

The figure your lender quotes to settle is not the balance the schedule reaches. A rebate separates them, and it is set by a published formula this pagedeliberately does not implement and does not approximate. What this page publishes instead is the difference between your quote and that balance, stated as its own figure, so you can see what the quote adds without this page pretending to derive it. A page that computed a settlement figure from a rule it had chosen would hand you a number your lender has not agreed to, and nothing on it could tell you so.

The limits this calculation imposes on itself

• Every figure is yours. This page publishes no liability share, no settlement figure, no valuation and no charge, and there is no field that could carry one. One half is the ordinary case for the share everywhere this mechanism exists, and it is deliberately not this page’s assumption — the whole finding is that the figure is misread, and supplying it would be publishing one jurisdiction’s rule as though UBWHY had established it.
• The settlement figure is a quote, not a computation. The rebate that separates a quoted settlement from the balance the schedule reaches is a published formula this page deliberately does not implement and does not approximate. What it publishes instead is the difference between your quote and that balance, so you can see what the quote adds without this page claiming to derive it.
• The resale value and the return charges are yours. This page holds no valuation model and no condition or mileage schedule, and it has no way to check either figure — it compares them, which is the part nothing else combines.
• The schedule is the ordinary one. A level monthly payment on a balance charged monthly at the rate you entered, ending at the optional final payment. The monthly payment and the outstanding balance are imported from the parent model rather than restated here, so the total this page prints and the balance it reads are the same arithmetic.
• Whether your agreement carries a termination right at all, and on what terms, is a question about your agreement. This page computes what reaching a stated share of a stated total would take; it does not know, and does not assert, that you are entitled to anything.

What is not modelled

• any country, jurisdiction, statute, regulator or termination right — the share you are liable for is a figure you enter, not one this page holds
• the statutory rebate that separates a quoted settlement figure from the balance outstanding
• what any vehicle is worth, now or at any other time
• what an excess mileage or condition assessment would actually come to
• any lender, finance product, insurance product or place to sell a vehicle
• whether your agreement carries a termination right, or on what terms
• what you would drive afterwards, or what replacing the vehicle would cost
• anything about tax, at any time

The discipline the second half of this page needs — that two costs are only comparable when what you hold at the end of each is the same — is taught in the explainer:how to compare two financial uses of money. That explainer is about choosing where to put money and this page is about getting out of an agreement; what they share is the rule that a comparison needs a common end state, and it is the rule that decides which two of these three routes may be ranked.