Earning and spending · Gains et dépenses
| English | Français |
|---|---|
| gross pay/ɡrəʊs peɪ/ | salaire brut |
| deductions/dɪˈdʌkʃnz/ | retenues |
| net pay/net peɪ/ | salaire net |
| simple interest/ˈsɪmpl ˈɪntrest/ | intérêt simple |
| compound interest/ˈkɒmpaʊnd ˈɪntrest/ | intérêts composés |
| discount/ˈdɪskaʊnt/ | remise |
Start with the stated pay rules
- Gross pay 税前工资 is pay before deductions 扣除项; net pay 税后工资 is what remains after those deductions. A cash budget should account for the amount available and the timing of receipts and expenses.
- Regular hours, overtime and commission may use different rules. Define their rates and bases before combining them; the practice rules are invented, not actual tax or employment conditions.
Which figure should a personal budget be built on? · Sur quel montant devrait être basé un budget personnel ?
Net is what actually arrives. A budget built on gross is short by the deductions before it starts. · Le net est ce qui arrive réellement. Un budget basé sur le brut sera insuffisant dès le départ par manque des déductions.
Match rate and period
- Simple interest 单利 uses · utilise $I=Prt$ on the original principal. Compound interest 复利 uses · utilise $A=P(1+r)^n$ under matching rate and period assumptions with no other cash flows.
- At the same positive rate over more than one completed period, compounding gives a larger final value than simple interest. Different rates, charges or payment schedules require an actual comparison.
At the same positive rate, with no other cash flows, why does compound interest exceed simple interest after more than one completed period? · Au même taux positif, sans autres flux de trésorerie, pourquoi l'intérêt composé dépasse-t-il l'intérêt simple après plus d'une période achevée ?
The base grows each period, which is what makes it geometric rather than arithmetic. · La base augmente chaque période, ce qui la rend géométrique plutôt qu'arithmétique.
Discounts act on a defined base
- A discount 折扣 of 20% uses multiplier 0.8. Successive 20% and 10% discounts use $0.8(0.9)=0.72$, a 28% reduction.
- To reverse a 10% discount, divide the sale price by 0.9. Apply a later delivery fee separately unless the question explicitly discounts that fee too.
After a 10% discount a coat costs 234. What was the original price? · Après une remise de 10 %, un manteau coûte 234. Quel était le prix original ?
234 ÷ 0.9 = 260. To reverse a percentage change you divide, never add the same percentage back. · 234 ÷ 0.9 = 260. Pour inverser une variation en pourcentage, vous divisez, n'ajoutez jamais le même pourcentage.
What single multiplier represents a 25% increase? · Quel unique multiplicateur représente une augmentation de 25 % ?
The original 100% plus 25% more. Turning percentages into multipliers first prevents most errors in this unit. · Les 100 % initiaux plus 25 % de plus. Transformer les pourcentages en multiplicateurs d'abord évite la plupart des erreurs dans cette unité.
Compare delivered totals. A 500-unit item with 20% off and 30 delivery costs $T_A=500(0.8)+30=430$. Two successive 10% discounts with free delivery give $T_B=500(0.9)^2=405$. Under the stated identical-item and no-other-charge assumptions, B is cheaper by 25 units.
240 rises by 15%, then the new price falls by 15%. What is the final value, to 2 decimal places? · 240 augmente de 15 %, puis le nouveau prix diminue de 15 %. Quelle est la valeur finale, à 2 décimales près ?
240 × 1.15 × 0.85 = 234.60. The two percentages act on different amounts. · 240 × 1.15 × 0.85 = 234.60. Les deux pourcentages s'appliquent à des montants différents.
A lower unit price may require more spending. A pack of 12 for 30 costs 2.50 per item; 20 for 46 costs 2.30 per item. Compare both unit price and the required quantity. Sheet 2.2 also checks overtime, commission and a maximum acceptable fee.
For an invented rule charging 20% only on the amount above a threshold, apply it only to that excess. This wording does not establish a real tax schedule. Do not turn a classroom threshold example into a universal financial rule.
An invented rule charges 20% only on earnings above a threshold. A person above that threshold pays 20% of their whole income. · Une règle inventaire applique 20 % seulement sur les revenus dépassant un seuil. Une personne au-dessus de ce seuil paie 20 % de son revenu total.
Under the explicitly stated teaching rule, only the excess above the threshold is charged. This does not define an actual tax schedule. · Selon la règle d'enseignement explicitement énoncée, seul l'excédent au-dessus du seuil est taxé. Cela ne définit pas un véritable barème fiscal.