Liquidated damages cap: the tenth late week costs and the eleventh nothing

A deduction runs at 0.5% a week and stops at 5%. On a basis of 10,000,000 that is 50,000 a week, and week 10 reaches the ceiling of 500,000. Week 11 adds nothing, and so does week 20, which is the reverse of the pressure the schedule was written to apply. Move the ceiling from 2% to 20% and the last week that costs anything moves from week 4 to week 40. Zero here is a further deduction of zero on the schedule you typed, and nothing else.

Live result

The checked week adds 0 and brings the running total to 500,000.

Checked week11
Smallest breaker week11

Once the running percentage reaches the cap, a further late week adds nothing to the schedule.

The rule as commonly stated

Every additional late week adds one full weekly deduction.

The typed rate, cap, week count, and hypothetical monetary basis describe the same unchanged scope and information state. The basis scales the percentages into whole money only and does not change the schedule shape.

Try a scenario

The cap and the week where the rule breaks

Cap%

The sweep below moves only this cap.

Smallest breaker week: 11

The typed schedule

Weekly rate%

Checked weekweeks

The computable witness

Full weekly amount: 50,000
Cap amount: 500,000
Cumulative amount: 500,000
Amount added at checked week: 0 · zero additional deduction
Smallest breaker week: 11
Last week adding any amount: 10
First zero week: 11

\Delta A_w = A_w-A_{w-1}

where $\Delta A_w$ is the marginal amount, $A_w$ the amount in the week, and $A_{w-1}$ the amount in the preceding week.

Weeks 9, 10 and 11 in the worked record

Week 9 adds the full 50,000 and reaches 450,000. It does not break the rule.

50,000

Week 10 adds the full 50,000 and reaches the 500,000 cap. It still does not break the rule.

50,000

Week 11 adds zero. It is the smallest breaker.

The restoring condition

For a checked week strictly before week 11, the cap has not shortened that week's full increment and the commonly stated rule holds for that checked week.

It computes marginal arithmetic from a typed rate, cap, week count, and hypothetical basis. Zero additional deduction does not make lateness lawful or costless, and the result decides no entitlement or contractual effect.

Here is the maths

Hypothetical monetary basis

Shown in $. The arithmetic is identical in any single currency.

The formula, in words

Multiply the checked week by the weekly rate and stop the running percentage at the cap. Convert the running percentage to a whole amount on the hypothetical basis. Subtract the amount at the preceding week from the checked week amount. The smallest breaker is one more than the cap divided by the rate and rounded down. If the cap is not an exact multiple of the rate, that breaker carries a partial amount. Otherwise it carries zero.

p_w=\min\left(w\,r,c\right),\qquad \Delta A_w=A_w-A_{w-1},\qquad w_*=\left\lfloor\frac{c}{r}\right\rfloor+1

\begin{gathered}p_w=\min\left(w\,r,c\right), \\ \Delta A_w=A_w-A_{w-1}, \\ w_*=\left\lfloor\frac{c}{r}\right\rfloor+1\end{gathered}

where $p_w$ is the deduction percent in the week, $w$ the week number, $r$ the weekly rate, $c$ the cap, $\Delta A_w$ the marginal amount, $A_w$ the amount in the week, $A_{w-1}$ the amount in the preceding week, and $w_*$ the smallest breaker week.

A worked example

A 0.5% weekly rate on 10,000,000 is 50,000, and a 5% cap is 500,000.
Week 9 reaches 450,000. Week 10 adds 50,000 and reaches 500,000.
Week 11 remains at 500,000, so 500,000 minus 500,000 is 0. Week 11 is the first breaker.

What this does not model

It does not decide whether a schedule applies, whether the count is lawful or excused, whether sections have separate caps, or what other cost or consequence continues after the cap. Independently typed sections are calculated separately and are never combined here.

What the sweep holds fixed

Only cap percentage moves. Weekly rate, checked week, and hypothetical basis stay fixed. At a 0.5% rate, the last week adding an amount moves from week 4 at a 2% cap to week 40 at a 20% cap.

Source class

The public source class is capped delay deduction schedules in supply and construction contracts, described only through a visitor typed rate, cap, and elapsed week structure. No clause, regime, authority, definition, or legal interpretation is reproduced.

Calculation version

1.0.0

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This counterexample describes only the arithmetic shape of a capped weekly deduction schedule. It never interprets a contract, classifies lateness, decides entitlement, treats delay as excused, combines sections, or identifies other consequences. A zero here means a further deduction of zero under the schedule typed on this page and nothing else.

Capped weekly deduction witness