Earning and spending
Introduced| English | Meaning |
|---|---|
| gross pay/ɡrəʊs peɪ/ | gross pay |
| deductions/dɪˈdʌkʃnz/ | Amounts subtracted from gross earnings, such as taxes or pension contributions, when calculating take-home pay. |
| net pay/net peɪ/ | Earnings remaining after taxes and other payroll deductions have been subtracted from gross pay. |
| simple interest/ˈsɪmpl ˈɪntrest/ | Interest calculated only on the original principal, without adding previous interest to it. |
| compound interest/ˈkɒmpaʊnd ˈɪntrest/ | Interest calculated on the original principal together with previously accumulated interest. |
| discount/ˈdɪskaʊnt/ | A reduction from an item's original or stated price. |
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?
Difficulty 1/5 · 100 coins + a small bonus on first completion today
Net is what actually arrives. A budget built on gross is short by the deductions before it starts.
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?
Difficulty 1/5 · 100 coins + a small bonus on first completion today
The base grows each period, which is what makes it geometric rather than arithmetic.
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?
Difficulty 2/5 · 140 coins + a small bonus on first completion today
234 ÷ 0.9 = 260. To reverse a percentage change you divide, never add the same percentage back.
What single multiplier represents a 25% increase?
Difficulty 1/5 · 100 coins + a small bonus on first completion today
The original 100% plus 25% more. Turning percentages into multipliers first prevents most errors in this unit.
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?
Difficulty 2/5 · 140 coins + a small bonus on first completion today
240 × 1.15 × 0.85 = 234.60. The two percentages act on different amounts.
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.
Difficulty 1/5 · 100 coins + a small bonus on first completion today
Under the explicitly stated teaching rule, only the excess above the threshold is charged. This does not define an actual tax schedule.