Compare Stacked Store Discounts Before Tax

Multiply the remaining portions

Starting at $100, a 20% discount leaves $80. A further 10% discount removes $8 and leaves $72. The combined factor is 0.80 × 0.90 = 0.72, equivalent to a 28% discount. For any sequence, multiply all (1 − discount/100) factors rather than adding rates.

Compare the actual payable bases

A single 30% discount leaves $70, which is $2 less than the stacked 20% and 10% offer on the same $100 item. Fixed-dollar coupons require a separate subtraction and may be applied before or after percentage discounts; the retailer’s rule determines the order.

Choose the tax base

For an illustrative 8% tax applied to the discounted $72, tax is $5.76 and total is $77.76. If a rule instead taxed the original $100, tax would be $8 and total $80. The calculator’s selected arithmetic model does not establish local tax law or coupon treatment.

Understand which operations commute

Pure percentage discounts multiply, so 20% then 10% gives the same unrounded result as 10% then 20%. A fixed $10 coupon does not generally commute with 20%: $100 × 0.8 − $10 = $70, while ($100 − $10) × 0.8 = $72. Intermediate cent rounding can also create small differences.

Verify against the receipt

Check excluded items, quantity limits, shipping and whether the displayed percentage applies to a list price that differs from the current selling price. Keep unrounded calculations for comparison, then read the retailer’s line-by-line rounding rules when a checkout total differs by a cent.

Compare another stacked offer with a single discount

Start with a price of $240, apply 25% off, then another 15% off the remaining price. The first step leaves $180 and the second leaves $153. Multiplying 0.75 × 0.85 gives 0.6375, so the effective discount is 36.25%, not forty percent. Before tax, savings are $240 − $153 = $87. A single forty-percent discount would leave $144 and save $96, nine dollars more under the same starting price.

At an illustrative eight-percent tax on the discounted price, the stacked offer totals $153 × 1.08 = $165.24. Enter 25 in the first discount field and 15 in the additional successive-discount field. Do not enter the already combined 36.25 alongside another fifteen-percent discount, which would apply the second promotion twice. A single combined field is equivalent only when no additional discount remains.

Inspect a fixed coupon as a different operation

A $30 fixed coupon after a twenty-five-percent reduction on $240 gives $240 × 0.75 − $30 = $150. Applying the coupon first gives ($240 − $30) × 0.75 = $157.50. The seven-dollar-fifty difference arises because the percentage reduction affects the coupon amount only in the second ordering. The successive-percentage form does not implement a fixed-dollar coupon; calculate that separate operation according to the retailer’s written sequence.

Two pure twenty-percent discounts, by contrast, leave 0.80 × 0.80 = 0.64 of the price, an effective thirty-six-percent reduction. Reversing two pure percentage factors produces the same unrounded product. Shipping charges, fixed fees and minimum-order conditions may break that simple comparison because they are not percentage factors acting on the identical base. List the operations rather than treating every advertised saving as another rate to add.

Quantify a one-point change in the second discount

After the initial twenty-five-percent discount, the remaining base is $180. Increasing the second discount from fifteen to sixteen percent reduces the pre-tax amount by $1.80. With eight-percent tax applied afterward, the payable reduction is $1.80 × 1.08 = $1.944 before currency rounding. This is a one-percentage-point change in the second rate, not an extra one percent of the original $240.

Holding the discounted base at $153, increasing the entered tax from eight to nine percent adds $1.53 before rounding. These sensitivity calculations hold other conditions constant. They do not identify a legally applicable tax base or determine whether a coupon changes that base. Use the actual receipt rules for those choices, then inspect the arithmetic; the calculator’s entered tax rate is not an automatic jurisdiction selector.

Explain a receipt difference with explicit rounding stages

A five-cent price reduced by ten percent twice has an exact final value of $0.05 × 0.90 × 0.90 = $0.0405. Rounding only the final amount to cents gives four cents. If a retailer rounds each intermediate amount upward at a half-cent midpoint, the first $0.045 becomes five cents and the second does the same, leaving five cents. The operations commute algebraically, but a rounding operation inserted between them changes the model.

Keep the original price, promotion eligibility, percentage sequence, fixed coupons, tax base and rounding stages beside a comparison. Savings displayed to cents are a presentation choice unless a payment-stage rule is stated. A blank additional-discount field means no extra reduction, while an out-of-range rate is rejected. The tool does not verify whether a list price is genuine, whether promotions can be combined or whether a particular product qualifies.