Lesson Guide
Explanation
Business runs on two numbers: the COST price (CP — what the shop paid, $60) and the SELLING price (SP — what the customer pays, $84). Sell above cost and the difference is PROFIT ($24); below cost, LOSS. The Y8 upgrade: profit as a PERCENTAGE, always measured against the COST price — 24/60 × 100 = 40% profit. Why cost? Because that's what the shop risked. Dividing by the selling price is this topic's version of the wrong-original trap.
Your Turn
A card bought for $8 sells for $14. Profit and profit %? Check: $6; 6/8 = 75%.
Watch Out
Profit % uses the COST price as the base, even though the selling price is usually mentioned last. Anchor on what was PAID first.
Explanation
Shops price by MARKUP — a percentage increase on cost. Cost $45 marked up 60%: SP = 45 × 1.6 = $72. It's your multiplier machine wearing a suit: +150% → ×2.5, doubling → ×2 (a 100% markup). And it reverses the same way: selling at $72 with a 60% markup means cost was 72 ÷ 1.6 = $45. Markup percentage and profit percentage are the same number, both measured on cost.
Your Turn
Cost $80, markup 35% — selling price? And SP $90 with 50% markup — cost? Check: $108; and 90 ÷ 1.5 = $60.
Watch Out
A 150% markup means ×2.5 (you add 1.5 to the 1) — not ×1.5. Markups over 100% are routine in retail.
Explanation
Discount is a percentage decrease on the ticket price: $120 sneakers at 25% off → 120 × 0.75 = $90. Follow a full retail story: shop buys at $60, marks up 100% (ticket $120), then discounts 25% (sale $90) — and still banks 50% profit on cost. Sales are less generous than they look! And stacked discounts multiply, never add: '25% off then a further 10% off' is 0.75 × 0.9 = 0.675 — 32.5% off, not 35%.
Your Turn
A $250 jacket: 30% off, then a further 10% off at the register. Final price and true total discount? Check: 250 × 0.7 × 0.9 = $157.50 → 37% off.
Watch Out
'Further 10% off' applies to the ALREADY-discounted price. Adding discount percentages flatters the deal — multiply the multipliers.
Explanation
Banks pay (and charge) interest — money that money earns. SIMPLE INTEREST uses I = P × r × t: Principal (the money deposited), rate per year AS A DECIMAL (4% → 0.04), time IN YEARS. $2000 at 4% p.a. for 3 years: I = 2000 × 0.04 × 3 = $240, making $2240 in total. 'Simple' means the same interest every year — the earnings never earn. Watch the units: 18 months is t = 1.5, not 18!
Your Turn
I for $5000 at 3% p.a. for 4 years — and the total? Check: 5000 × 0.03 × 4 = $600; total $5600.
Watch Out
Two unit conversions before the formula: rate → decimal, months → years. 6% for 30 months is 0.06 and 2.5.
Explanation
The formula runs backwards for any missing letter — no algebra needed, just per-year thinking. Missing RATE: $3000 earned $360 over 4 years → $90 per year → 90/3000 = 3% p.a. Missing TIME: $2000 at 5% earns $100 a year → $500 needs 5 years. Missing PRINCIPAL: $180 earned at 4% over 3 years → 12% of P is 180 → unitary: P = $1500. Everything reduces to 'how much per year?' plus the unitary method you already own.
Your Turn
$4000 earned $480 in 2 years — what rate? Check: $240/year → 240/4000 = 6% p.a.
Watch Out
Always step through per-year amounts — jumping straight to formula-shuffling is where signs and units get scrambled.
Explanation
Your complete money toolkit: profit % (on cost!), markup (×(1+m)), discount (×(1−d)), stacked changes (multiply multipliers), simple interest (I = Prt), and reverse problems (name the survivor percentage, then unitary). Every money problem starts the same way: identify the BASE the percentage acts on — the cost, the ticket price, or the principal. Get the base right and the tools do the rest. This is the maths of every shop, bank and payslip you'll ever meet. Quiz and exercises!
Your Turn
Gauntlet: bought $40, marked up 50%, then 20% off — profit or loss, and how much? Check: 40 → 60 → 48: $8 profit (20% on cost).
Watch Out
Each percentage in a chain may have a DIFFERENT base. Slow down at every % sign and ask: percent of WHAT?
📌 Key Points — this lesson in a nutshell
- Profit = SP − CP; a loss is when SP < CP. Percentage profit is always on the COST price.
- Markup and discount are multipliers: ×(1 + m) up, ×(1 − d) down.
- Simple interest: I = P × r × t, with r as a decimal and t in years.
- Total to repay = principal + interest.
- Rearrange I = Prt to find whichever of P, r or t is missing.
Step 1: Introduction
Step 1 of 6
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