Earning and spending · 收入与消费
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| gross pay/ɡrəʊs peɪ/ | 税前工资 | shuì qián gōng zī |
| deductions/dɪˈdʌkʃnz/ | 扣除项 | kòu chú xiàng |
| net pay/net peɪ/ | 税后工资 | shuì hòu gōng zī |
| simple interest/ˈsɪmpl ˈɪntrest/ | 单利 | dān lì |
| compound interest/ˈkɒmpaʊnd ˈɪntrest/ | 复利 | fù lì |
| discount/ˈdɪskaʊnt/ | 折扣 | zhé kòu |
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? · 个人预算应该以哪个数字为基础?
Net is what actually arrives. A budget built on gross is short by the deductions before it starts. · 税后才是真正到手的。按税前做预算,一开始就少了扣除项那部分。
Match rate and period
- Simple interest 单利 uses $I=Prt$ on the original principal. Compound interest 复利 uses $A=P(1+r)^n$ 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? · 在相同正利率且无其他现金流的情况下，为何复利在超过一个完整计息期后会高于单利？
The base grows each period, which is what makes it geometric rather than arithmetic. · 每一期的计息基数都在变大,这正是它属于等比而非等差的原因。
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? · 打折10%后一件外套售价234。原价是多少？
234 ÷ 0.9 = 260. To reverse a percentage change you divide, never add the same percentage back. · 234 ÷ 0.9 = 260。还原百分比变化要用除法,绝不是把同样的百分比加回去。
What single multiplier represents a 25% increase? · 上涨 25% 对应的单一乘数是多少?
The original 100% plus 25% more. Turning percentages into multipliers first prevents most errors in this unit. · 原来的 100% 加上多出的 25%。先把百分比化成乘数,能避免本单元的大多数错误。
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上涨15%后，新价格又下降15%。最终结果是多少？保留2位小数。
240 × 1.15 × 0.85 = 234.60. The two percentages act on different amounts. · 240 × 1.15 × 0.85 = 234.60。两个百分比作用在不同的基数上。
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. · 一项虚构规则仅对超过阈值的收入征收20%。但处于该阈值以上的人需对其全部收入缴纳20%。
Under the explicitly stated teaching rule, only the excess above the threshold is charged. This does not define an actual tax schedule. · 根据明确规定的征税规则，仅对超过阈值的部分征税。这并不构成实际的税率表。