Successive discounts compounded · Otherworld Labs · printed

Otherworld·Labs Trade pricing

What each reduction in your chain leaves, and the single rate your whole chain works out at

A chain of reductions is not worked out by adding the rates up. Each reduction works on what the one before it left, so the rate a whole chain works out at is read off the price the chain leaves and never from the rates added together, and this page prints both figures so that whatever gap there is between them, wide or none at all, is on the screen rather than in your head.

Six readings come off one typed chain: the price each reduction leaves and the amount it takes off, the net price at the end, the single rate the whole chain works out at, the list price that reaches a net you type, the rate taken from a list price to a net you both type, and the extended total at a quantity you type.

Every list price, every rate, every target, every quantity and every rounding increment is yours. The page proposes none of them, holds no typical, standard, industry or seasonal rate, works out no cost, no margin and no markup, and computes no tax of any kind.

The first block arrives holding a worked chain, which shows the arithmetic plainly and is not a rate this page proposes: type your own over it. The two blocks after it arrive with nothing typed in them but the rounding increment, which ships at nought because nought means none, so the net price you are checking against and the quantity are yours to type, and until each one is typed the reading that needs it says what it is waiting for in its own tile instead of printing a figure.

What this page does: from a list price and the reductions you type in the order they apply, it works out the price each reduction leaves, the amount it removes, the net price at the end, and the one rate the whole chain works out at, computed from the compounded chain and never from the rates added together. It runs the other way too: the list price that arrives at a net price you type on that chain, and the rate taken from a list price to a net price you both type. What it does not do: it proposes no rate and holds no typical, standard, industry or seasonal figure; it computes no tax of any kind - no sales tax, no VAT, no GST, no deduction - and holds no rate for one; it supplies no fee, no platform charge and no card or payment-processing figure; it works out no cost, no margin and no markup, and there is no field on it for a cost. It says nothing about whether a price is fair, competitive, advertisable or compliant, nothing about reference prices or sale-pricing rules, and nothing about what to discount or by how much. It converts no currency and holds no exchange rate. Nothing you type leaves your browser.

The walkthrough is on. Each part says what its figures are and where you find them. Turn it off at the top once you know your way around. The chain in the blanks is a worked example, kept because it is the chain that shows the arithmetic plainly, and it is not a recommendation: this page proposes no rate and holds no typical, standard, industry or seasonal figure. Type your own over it and every figure here follows.

The net price this chain leaves$720.00
The single rate this whole chain works out at28.00%
The list price that reaches the net you typedno net price typed yet
The rate from your list price to the net you typedno net price typed yet
The extended total at the quantity you typedno quantity typed yet
A

The list price, and the reductions in the order they apply

Two things, both of them off the paper in your hand. The list price is the figure before anything comes off it. The reductions are the rates as the quote writes them, in the order they apply: a quote reading less twenty and ten is two reductions, the first one off the list and the second one off what the first one left.

The list price
The figure the reductions come off: the list, the book price, the price before the deal. A single figure, in whatever currency you are working in - this page prints no currency symbol of its own meaning and converts nothing.
How many reductions
Up to six. The count you type is also what decides how many rate boxes this page reads: set it back to two after filling four and the last two are put away, their figures stay in the boxes where you typed them, and nothing in them is applied while the count says two. Nought is a real answer and means no reduction at all, which prints the list price as the net and prints no single rate.
Each rate
The rate at that point in the sequence, read off the quote. The box takes a figure past a hundred and a minus figure on purpose, because both are real things somebody is handed and this page prints what they do instead of refusing them: a rate past a hundred takes off the whole price and keeps going, which leaves a minus price, and a minus rate is an increase and says so.
The list price the figure before anything comes off it
How many reductions nought to six, in the order they apply
Reduction 1The rate at this point per cent; a minus figure is an increase
Reduction 2The rate at this point per cent; it applies to what the one before it left

Every rate here is read off your own quote, price list or invoice. This page holds none of its own: no typical rate, no standard rate, no industry rate, no seasonal rate, and no view on what to discount or by how much. If the paper in your hand does not say it, this page cannot tell you it.

B

The chain, one reduction at a time

One row for each reduction, in the order you typed it: the rate, the amount that reduction takes off, the price it leaves, and the single rate the chain works out at by that point. The foot is the whole chain.

In the chainThe rateTaken off hereWhat it leavesThe chain by here
Reduction 120.00%$200.00$800.0020.00%
Reduction 210.00%$80.00$720.0028.00%
The whole chain—$280.00$720.0028.00%

That arithmetic written out, one line at a time. Every price in the chain is worked from the list price and the rates, not from the price before it, so no figure here is worked from a rounded one.

1The price reduction 1 leaves1,000.00 x 80.00 / 100$800.00
2What reduction 1 took off1,000.00 - 800.00$200.00
3The price reduction 2 leaves1,000.00 x 80.00 x 90.00 / 100 / 100$720.00
4What reduction 2 took off800.00 - 720.00$80.00
5The whole amount taken off1,000.00 - 720.00$280.00
C

The single rate, and the sum it need not be

The one figure this page is for. The single rate a chain works out at is read from what the chain actually leaves and never from the rates added together, because each rate works on what the one before it left instead of on the list. Any gap between the two figures is a result of the chain you typed, and the sentence this block prints with them reads the two as they stand at the state you are in.

Added together the rates you typed come to 30.00%. Applied one after another, in the order you typed them, they come to 28.00%, because each one works on what the one before it left.

6The chain as one rate by reduction 1100 - 800.00 x 100 / 1,000.0020.00%
7The chain as one rate by reduction 2100 - 720.00 x 100 / 1,000.0028.00%
8The single rate this whole chain works out at100 - 720.00 x 100 / 1,000.0028.00%
9The rate from your list price to the net you typedwaiting for the net price you are checking against—

This arithmetic, written out for anything reading the page instead of looking at it: api.json beside this page carries every input, every output, the rounding, the identities, three worked chains and a list of what the calculation deliberately leaves alone.

D

The other direction: a net you type

Two readings that start from a net price instead of ending at one. Type the net you are checking against and this page works out the list price that would arrive at it on that chain, and the rate taken from the list price you typed to that net. Both wait until a net is typed, and neither prints a nought in the meantime.

The net you type
The figure on the invoice, or the price somebody is asking you to accept. Leave it empty and the two readings that need it stay empty too.
Why a list price can be out of reach
A rate of exactly a hundred leaves nothing from any list price at all, so on a chain carrying one no list price arrives at a net of anything but nothing. A chain that ends up putting the price up would need a minus list price to arrive at a net the list itself has already passed. This page says so instead of printing a figure.
The net price you are checking against leave it empty for none
E

The quantity, and the rounding increment you keep to

Two figures of your own that change what prints. The quantity extends the net price across a line of a purchase order or a shelf tag. The rounding increment is your own house rule for where a price is allowed to land; this page has no rounding rule of its own and applies none until you type one.

The quantity
How many of the thing the price is for, off the purchase-order line or the count of units being tagged. Whole units. Leave it empty and the extended total stays empty.
The rounding increment
The step your own prices are allowed to sit on: five cents, ten cents, a whole unit. Nought, which is how it ships, means no increment at all and the net price prints to the cent. The chain itself is never worked from a rounded figure: the increment is applied once, at the end, to the net price, and the row that applies it says so.
The quantity whole units; leave it empty for none
Your rounding increment nought means none, which is how it ships
10The list price that reaches the net you typedwaiting for the net price you are checking against—
11The extended total at the quantity you typedwaiting for the quantity—
12The net price on your own incrementno increment is typed, so none is applied—
F

Words that come up

List price
The figure the reductions come off. Nothing on this page works it out for you; it is typed.
A chain of reductions
The rates you type, applied one after another, each to what the one before it left. One rate is a chain of one, and no rate typed is a chain of none; the page says so in words where it prints them, and the compounding this page is for opens from the second rate onward. A quote reading less twenty and ten is a chain of two.
The price a reduction leaves
The list price multiplied by what each rate so far leaves of it, kept to the cent. Every one of them is worked from the list price and the rates instead of from the printed price before it.
Taken off here
The drop from the price in the row before it to the price in this row, which is what that one reduction removed. The column adds to the whole amount taken off, because each figure in it is the difference of two printed prices.
The single rate a chain works out at
The one rate that takes a list price straight to the net the whole chain leaves. It is read from the net and the list, which is the compounded chain, and it is never the rates added together.
Net price
What is left at the end of the chain. With no reduction typed it is the list price itself.
The rate taken from a list to a net
The single rate between two figures you typed yourself, which is a different question from what your chain works out at: this one asks what rate you actually got, and the chain asks what rate your quote describes.
Extended total
The net price multiplied by the quantity you typed. The quantity is yours and this page proposes none.
Rounding increment
A step of your own that the net price is moved onto once, at the end. This page holds no increment and applies none until one is typed.
The figures print with it. Nothing is sent anywhere and nothing is saved except whether the walkthrough is on.

The price-change sheet a whole list goes on

This page takes one price and forgets it. What it cannot keep is the thing the two sides argue over when the invoice arrives: a dated row for every line on the quote, the chain each line was quoted at, and what that chain actually came to.

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