Percentages of money: discounts, tax and tips, worked out

Most percentages in everyday life are attached to money, and money percentages have a saving grace: they all run on one move. When I calculate percentage of money — a discount, a tax, a tip — I always translate the percentage into the multiplier it really is, then let one multiplication do the work. In this article I work a full set in US dollars: a 20% discount, an 8.25% sales-tax add-on, an 18% tip, a complete restaurant receipt end to end, and the stacked-discount trap that quietly costs shoppers real money. Think of this article as a percentage calculator money edition: every example is in US dollars, and every one runs on the single move in the next section.

The one move: turn the percentage into a multiplier

Here is how to calculate percentage of money amounts in either direction. Every money percentage is one of two shapes. Money coming off: a 20% discount means you pay 80% of the price, so multiply by 0.80. Money going on: an 8.25% tax means you pay 108.25% of the price, so multiply by 1.0825. Once you see percentages of money this way, you never need the two-step “find the percentage, then add or subtract it” dance again — although I will show both routes in the first example so you can see they agree.

Discounts: 20% off an $85 jacket

The two-step route: 20% of $85 is 0.20 × 85 = $17 off, so you pay 85 − 17 = $68. The multiplier route: 85 × 0.80 = $68, one step. Here is the same jacket at the discount rates shops actually use:

Every row computed on the $85 tag price. Notice the “you pay” column is the multiplier column: at 30% off you pay 70%, and 0.70 × $85 = $59.50.

Sales tax: a percentage on top

Tax runs the other direction. On a $120 purchase with an 8.25% rate — an example rate in the range many US shoppers actually pay, since real rates vary by state and city — the tax is 0.0825 × 120 = $9.90, and the register total is 120 + 9.90 = $129.90. The multiplier version: 120 × 1.0825 = $129.90 in one step. Working backwards works too: if a receipt total of $129.90 already includes 8.25% tax, the pre-tax price is 129.90 ÷ 1.0825 = $120.00 exactly — dividing by the multiplier undoes it, while subtracting 8.25% of $129.90 would give you the wrong price.

The same purchase at four tax rates

Because real US sales-tax rates vary by state, county and city — combined rates run from under 5% in some places to over 10% in others, as of 2026 — here is what three typical purchases cost at four example rates spanning that range. Each cell shows the tax, with the register total in parentheses, rounded to the nearest cent:

Tax and totals computed as amount × rate and amount × (1 + rate). Rates are illustrative examples across the US range, not quotes for any specific jurisdiction.

Two things are worth noticing. The $300 purchase shows the stakes: the gap between a 6% and a 10% jurisdiction is $12 of tax on one item, which is why big-ticket purchases near a state or county border really do change price at the register. And the rounding is real, not decorative — 8.25% of $50 is exactly $4.125, which the register rounds to $4.13, so totals on genuine receipts can differ by a cent from a naive calculation without anything being wrong.

Tips: percentage of the bill

A tip is a percentage you choose. On a $64 restaurant bill, the customary range computes like this:

Tips computed on the $64 pre-tax bill, the convention I use and the one most guides recommend.

The mental shortcut for the middle row: 10% of $64 is $6.40, half of that (5%) is $3.20, and a 20% tip is just double the 10% figure — $12.80 — with 18% sitting a little under it. Our tip calculator handles the full version of this, including splitting the total between people, which is where restaurant arithmetic usually falls apart.

One receipt, end to end

Now stack the shapes in the order a real bill stacks them. Dinner comes to $64.00. Tax at our example 8.25% adds 0.0825 × 64 = $5.28. I tip 18% on the pre-tax $64 — $11.52 — because the tip rewards the service, not the tax. Total: 64.00 + 5.28 + 11.52 = $80.80. Two of the three lines are percentages of the same $64 base, which is why they can be added directly. The moment a percentage is taken of a number that already includes another percentage, that stops being true — which brings me to the trap.

Saving a percentage of money: the budget version

The same move runs your budget in reverse. If your take-home pay is $2,900 a month and you save 15% of it, the multiplier gives the transfer in one step: 2,900 × 0.15 = $435 a month, which is $5,220 across a year. The neighbouring rates show why the percentage matters more than the dollar figure at first glance: at 10% you would move $290 a month ($3,480 a year), and at 20% you would move $580 a month ($6,960 a year) — the five-point step from 15% to 20% is worth $1,740 a year on the same paycheck. Percentages of money are how budgets are usually written, precisely because they scale with your income while a fixed dollar amount does not.

The stacked-discount trap

Cash back: the percentage that runs in your favour

Not every percentage at the register works against you. A card paying 5% cash back on that $92.47 grocery total returns 92.47 × 0.05 = $4.62, bringing your effective cost to $87.85. The arithmetic is the multiplier rule once more — you effectively paid 95% of the total — but the psychology is the mirror image of the stacked discount: a percentage of a number you have already paid feels smaller than the same percentage off the price would have, even when the dollars are comparable. Judging offers in dollars rather than in percentages is the habit that survives all of these framings.

A bigger stacking example, and splitting the result

The trap scales with the ticket. A $250 coat is marked 40% off in a sale, and you hold a coupon for an extra 15% off. The sale takes it to 250 × 0.60 = $150; the coupon then removes 15% of $150 — $22.50 — leaving $127.50. Had the two percentages truly added to 55% off, you would have paid $112.50. The effective discount is (250 − 127.50) ÷ 250 = 49%, not 55%, and the $15 gap between the imagined price and the real one is pure wrong-base arithmetic. Retailers stack percentages precisely because each additional layer sounds bigger than it is.

And when the bill finally lands, one more everyday division: split the $80.80 receipt from earlier between four people and each share is 80.80 ÷ 4 = $20.20 exactly. Between three people it is $26.93 each with a cent left over — 3 × 26.93 = $80.79 — which is why one person at every group dinner quietly pays a cent more, and why splitting apps exist.

A whole cart, start to finish

Everything in this article, in one transaction. Your cart holds three items: $32.00, $48.50 and $19.99, a subtotal of $100.49. You have a 15% coupon, and your tax rate is our 8.25% example. Order matters, and the register’s order is: discount first, tax on what remains. The coupon removes 15% of $100.49 — $15.07 — leaving a discounted subtotal of $85.42. Tax is then charged on $85.42, not on the original $100.49: 8.25% of $85.42 is $7.05. Final total: 85.42 + 7.05 = $92.47. Had the tax been calculated before the coupon — as a few jurisdictions and many confused shoppers assume — the tax alone would have been $8.29 and the total $93.71. The $1.24 difference between the two orders is why “is the coupon applied before tax?” is a real question with a real answer, and why reading a receipt top to bottom, in the order the percentages were applied, is the only way to check one.

The general rule underneath everything in this article: percentages of money can only be added or subtracted when they share the same base. Discount then tax, tip on the pre-tax amount, tax-inclusive totals divided back out — each is just the multiplier rule applied carefully. When a deal’s percentages apply in sequence, multiply the multipliers: 0.80 × 0.90 = 0.72, which is why you pay 72% of the tag. If you would rather not chain multipliers in your head at the register, that is precisely the job our percentage calculator exists to do.

Sources: all figures computed for this article. The 8.25% sales-tax rate is an illustrative example — actual US rates vary by state, county and city; check your local rate for a real purchase.