Earning and spending
| English | Chinese | Pinyin |
|---|---|---|
| gross pay | 税前工资 | shuì qián gōng zī |
| net pay | 税后工资 | shuì hòu gōng zī |
| deductions | 扣除项 | kòu chú xiàng |
| compound interest | 复利 | fù lì |
| simple interest | 单利 | dān lì |
| discount | 折扣 | zhé kòu |
What actually arrives
- A salary of 12,000 a month is not 12,000 in your account.
- Gross pay 税前工资 is what you earn. Net pay 税后工资 is what arrives after deductions 扣除项.
- Every budget in GAC034 starts from net, and a budget built on gross is short before it begins.
Which figure should a personal budget be built on?
Net is what actually arrives. A budget built on gross is short by the deductions before it starts.
Simple and compound interest
- Simple interest 单利 pays on the original amount only: $I = Prt$.
- Compound interest 复利 pays on the interest too: $A = P(1+r)^n$.
- Over one period they agree. Over ten they do not, and the gap is the reason compound interest is what banks use.
Why does compound interest exceed simple interest over several years?
The base grows each period, which is what makes it geometric rather than arithmetic.
Discounts, and reversing them
- A discount 折扣 of 20% multiplies by $0.8$.
- Two discounts of 20% then 10% multiply by $0.8 \times 0.9 = 0.72$ — a 28% reduction, not 30%.
- To reverse a percentage change you divide. A price of 234 after a 10% discount was $234 \div 0.9 = 260$ before it.
After a 10% discount a coat costs 234. What was the original price?
234 ÷ 0.9 = 260. To reverse a percentage change you divide, never add the same percentage back.
What single multiplier represents a 25% increase?
The original 100% plus 25% more. Turning percentages into multipliers first prevents most errors in this unit.
A 15% rise, then a 15% fall, on 240 yuan.
Not 240. The rise applied to 240 and the fall applied to 276, so the two percentages acted on different amounts.
This is the most common percentage error in the whole programme, and the check is always the same: percentages of what?
240 rises by 15%, then the new price falls by 15%. What is the final value, to 2 decimal places?
240 × 1.15 × 0.85 = 234.60. The two percentages act on different amounts.
Turn every percentage into a multiplier before you calculate. Up 15% is ×1.15, down 15% is ×0.85, and a sequence of changes is the product of their multipliers. Multipliers compose; percentages do not.
Tax is usually charged in bands. A 20% rate above a threshold does not mean 20% of everything you earn — only 20% of the part above the threshold. A question giving you a threshold is testing exactly that, and answering with a flat percentage loses every mark.
If tax is 20% above a threshold, someone earning above it pays 20% of their whole income.
Only the part above the threshold is taxed at that rate. Applying it to everything is the standard error.