Earning and spending · Ingresos y gastos
| English | Español |
|---|---|
| gross pay/ɡrəʊs peɪ/ | salario bruto |
| deductions/dɪˈdʌkʃnz/ | deducciones |
| net pay/net peɪ/ | salario neto |
| simple interest/ˈsɪmpl ˈɪntrest/ | interés simple |
| compound interest/ˈkɒmpaʊnd ˈɪntrest/ | interés compuesto |
| discount/ˈdɪskaʊnt/ | descuento |
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? · ¿Sobre qué cifra se debe construir un presupuesto personal?
Net is what actually arrives. A budget built on gross is short by the deductions before it starts. · Lo neto es lo que realmente se recibe. Un presupuesto basado en el bruto tendrá un déficit debido a las deducciones antes de empezar.
Match rate and period
- Simple interest 单利 uses · usa $I=Prt$ on the original principal. Compound interest · Interés compuesto 复利 uses · usa $A=P(1+r)^n$ 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? · A la misma tasa positiva, sin otros flujos de efectivo, ¿por qué el interés compuesto excede al interés simple después de más de un periodo completado?
The base grows each period, which is what makes it geometric rather than arithmetic. · La base crece cada período, lo que la hace geométrica en lugar de aritmética.
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? · Después de un descuento del 10%, una chaqueta cuesta 234. ¿Cuál era el precio original?
234 ÷ 0.9 = 260. To reverse a percentage change you divide, never add the same percentage back. · 234 ÷ 0.9 = 260. Para revertir un cambio porcentual se divide, nunca se suma el mismo porcentaje nuevamente.
What single multiplier represents a 25% increase? · ¿Qué multiplicador único representa un aumento del 25%?
The original 100% plus 25% more. Turning percentages into multipliers first prevents most errors in this unit. · El 100% original más un 25% adicional. Convertir los porcentajes en multiplicadores primero evita la mayoría de errores en esta unidad.
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 aumenta un 15%, luego el nuevo precio disminuye un 15%. ¿Cuál es el valor final, redondeado a 2 decimales?
240 × 1.15 × 0.85 = 234.60. The two percentages act on different amounts. · 240 × 1.15 × 0.85 = 234.60. Los dos porcentajes actúan sobre cantidades diferentes.
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. · Una regla inventada cobra 20% solo sobre ganancias superiores a un umbral. Una persona por encima de ese umbral paga 20% de su ingreso total.
Under the explicitly stated teaching rule, only the excess above the threshold is charged. This does not define an actual tax schedule. · Bajo la regla de enseñanza explícitamente declarada, solo el exceso por encima del umbral está sujeto a cobro. Esto no define una tabla impositiva real.