How this instrument works
Three discounts in sequence do not add — each one takes its bite from whatever price the previous cut left behind. The first discount shrinks the original figure; the second shrinks that already-smaller number; the third shrinks it again. Multiply the three surviving fractions together and the price falls further with each added layer than a simple sum of percentages would ever suggest, because the base itself keeps shrinking underneath every additional cut.
This exact structure has a name outside the checkout aisle: a chain discount, or trade discount series, is how manufacturers and distributors quote net price to different tiers of buyer — a distributor discount, then a volume discount, then a prompt-payment discount, each applied to what the previous one left standing. A purchasing clerk reading a '20/10/5' series off a wholesale price list is running the identical multiplication a shopper runs when a storewide sale, a clearance markdown, and a loyalty coupon land on the same item at checkout.
The gap between the correct total and a naive addition widens every time a third layer joins the first two, which is exactly where most mental-math mistakes happen — people manage to remember that two discounts multiply, then forget the lesson the moment a third one appears and simply add it to the running total. This instrument only multiplies the three percentages against the figure you supply: it has no opinion on sales tax, shipping, restocking fees, or a fourth reduction added later, and it assumes each successive percentage is charged against whatever balance the one before it left standing, which is how nearly every real discount chain is actually built.
- Type the pre-discount figure into Original price, $ — the number none of the three cuts has touched yet.
- Set First discount, % to the initial markdown, such as a storewide sale or a wholesale distributor discount.
- Set Second discount, % to whatever applies next, calculated on what survived the first cut alone.
- Set Third discount, % for the final layer, applied to what remains after the first two have already run.
- Read Final price, $ for the actual amount owed once all three reductions have compounded in sequence.
Worked example — $1,000 at 20%, then 10%, then 5% off
Take a $1,000 item marked down 20% storewide, then a further 10% for a clearance category, then a final 5% loyalty-card discount at the register. The first cut leaves 1000 × 0.80 = $800. The second leaves 800 × 0.90 = $720. The third leaves 720 × 0.95 = $684.00 — the figure Final price, $ returns for exactly these inputs.
A shopper who simply adds 20, 10 and 5 to reach 35% off expects to pay $650.00, a $34.00 gap that grows wider as any of the three percentages grows. The true combined reduction is 31.6%, not 35%, because each discount shrinks the base the next one is measured against, so three stacked cuts always fall short of their own sum, and the shortfall compounds with every extra layer added to the chain.
Questions
Why doesn't 20% plus 10% plus 5% equal 35% off?
Because each percentage is taken from a shrinking base, not from the original price. The first cut leaves 80% of the price, the second leaves 90% of that, and the third leaves 95% of what remains — multiply those three fractions and 68.4% of the original survives, an effective 31.6% off rather than the 35% a straight addition implies. The gap widens as any single discount grows.
Does the order of the three discounts change the final price?
No. Multiplication does not care about sequence, so 20% then 10% then 5% lands on the same total as 5% then 20% then 10%. What can change a receipt is a store or vendor rule about which discount applies to which base — a coupon restricted to the pre-sale price behaves differently from one applied at the register, and that restriction, not the arithmetic, is what shifts the number.
What is a chain discount or trade discount series?
The same multiplication this sheet runs, used in wholesale and distributor pricing rather than retail. A manufacturer's list price might carry a published '20/10/5' series — a distributor discount, a volume discount, and a prompt-payment discount — each applied in turn to what the previous one left. Purchasing staff use it to convert a catalog list price into the net amount actually owed on a purchase order.
Where does sales tax fit into this calculation?
Nowhere — Final price, $ is only the outcome of three multiplications run against the figure you typed in. Registers generally charge tax on whatever amount survives all applicable markdowns, so work out Final price, $ here first, then treat any sales tax owed as a separate multiplication layered on top of that result, not blended into one of the three discount fields.
What if I only have two discounts, or a fourth one to apply?
Set the unused discount field to 0 and it drops out of the multiplication entirely, since a 0% cut leaves the price unchanged — useful for running this as a two-discount sheet. A fourth layer needs a second pass: copy the Final price, $ result, re-enter it as the next Original price, $, and put the fourth percentage into First discount, %.
Why is the third discount worth fewer dollars than the first?
Because it is a percentage of a smaller number. On the $1,000 example, the first cut removes $200, the second removes $80, and the third removes just $36 — the same 5% rate that would have removed $50 from the original price removes less once two earlier discounts have already shrunk the base it is measured against.
References
- Consumer Financial Protection Bureau — Consumer Tools
- U.S. Small Business Administration — Manage Your Business guide
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.