General Mathematics: Wages, Salaries, Commissions, Inflation, Markups, Discounts, and VAT

Comprehensive practice flashcards reviewing compensation calculations, overtime rates, commission structures, inflation and CPI, markups and discounts, and Value-Added Tax (VAT).

How is a salary defined, and what types of jobs typically receive it?

A salary is a fixed amount of payment received regularly (usually monthly) for performing a specific job, commonly for managerial, professional, or office roles where the compensation remains the same regardless of hours worked.

What is a wage, and how is it typically determined?

A wage is payment for work done based on time (such as hourly or daily rates) or output (number of pieces completed), common in manual labor or production work.

What is an allowance in employee compensation?

An allowance is an additional amount provided on top of a salary or wage to help cover specific personal or work-related expenses (e.g., transportation, meals, communication, housing) and is not considered payment for work done.

What standard assumptions are used for the number of working weeks and working hours per year?

It is assumed that $1\,\text{year} = 52\,\text{working weeks}$ and $1\,\text{week} = 40\,\text{working hours}$, resulting in $1\,\text{year} = 52 \times 40 = 2080\,\text{working hours}$.

What formula converts an annual salary to an hourly rate?

$$\text{Hourly Rate} = \frac{\text{Annual Salary}}{2080}$$

If Ben earns an annual gross salary of $\text{Php } 750,000.00$, what is his hourly rate rounded to two decimal places?

$$\text{Hourly Rate} = \frac{750,000.00}{2080} = \text{Php } 360.58$$

If Ben earns an annual gross salary of $\text{Php } 750,000.00$, what are his weekly, monthly, and bi-monthly salaries?

His weekly salary is $\frac{750,000.00}{52} = \text{Php } 14,423.08$, monthly salary is $\frac{750,000.00}{12} = \text{Php } 62,500.00$, and bi-monthly salary is $\frac{62,500.00}{2} = \text{Php } 31,250.00$.

Mrs. Mendoza is compensated at $\text{Php } 140.00$ per hour. How much are her annual and monthly salaries?

Her annual salary is $140.00 \times 2080 = \text{Php } 291,200.00$, and her monthly salary is $\frac{291,200.00}{12} = \text{Php } 24,266.67$.

What is the formula for calculating total pay including overtime on an ordinary working day?

$$\text{Total Pay} = \text{Daily Wage} + 125\%(\text{Hourly Rate})(\text{Number of Overtime Hours})$$

Under Philippine labor standards, how is compensation calculated for the first 8 hours and overtime hours on a rest day?

The first 8 hours are paid at $130\%$ of the daily wage ($\text{Daily Wage} \times 1.3$), and overtime is paid with an additional $30\%$ premium: $(130\%)(130\%)(\text{Hourly Rate})(\text{Number of Overtime Hours})$.

Jenna has a daily wage of $\text{Php } 750.00$. If she works 12 hours on her rest day, how much total compensation does she receive for that day?

Her basic hourly rate is $\frac{750.00}{8} = \text{Php } 93.75$. Her pay for the first 8 hours is $1.3 \times 750.00 = \text{Php } 975.00$. Her overtime pay for 4 hours is $1.3 \times 1.3 \times 93.75 \times 4 = \text{Php } 633.76$. Total pay is $975.00 + 633.76 = \text{Php } 1,608.76$.

What are the pay rates for work done on a Regular Holiday for the first 8 hours and for overtime hours?

The first 8 hours are paid at $200\%(\text{Daily Wage})$, and overtime is paid at $(200\%)(130\%)(\text{Hourly Rate})(\text{Number of Overtime Hours})$.

Jennie earns a monthly salary of $\text{Php } 16,500.00$. What are her annual salary, hourly rate, and daily wage?

Her annual salary is $16,500 \times 12 = \text{Php } 198,000.00$, her hourly rate is $\frac{198,000}{2080} = \text{Php } 95.19$, and her daily wage is $8 \times 95.19 = \text{Php } 761.52$.

How much does Jennie earn if she works 11 hours on Independence Day (a regular holiday), given a daily wage of $\text{Php } 761.52$ and an hourly rate of $\text{Php } 95.19$?

Her pay for the first 8 hours is $2.00 \times 761.52 = \text{Php } 1,523.04$. Her overtime pay for 3 hours is $2.00 \times 1.30 \times 95.19 \times 3 = \text{Php } 742.48$. Total pay is $1,523.04 + 742.48 = \text{Php } 2,265.52$.

A skilled worker earning a daily wage of $\text{Php } 1,200.00$ works 16 hours on a special non-working holiday that falls on a rest day. What is his total compensation for that day?

His hourly rate is $\frac{1,200.00}{8} = \text{Php } 150.00$. Pay for the first 8 hours is $1.50 \times 1,200.00 = \text{Php } 1,800.00$. Overtime pay for 8 hours is $1.50 \times 1.30 \times 150.00 \times 8 = \text{Php } 2,340.00$. Total pay is $1,800.00 + 2,340.00 = \text{Php } 4,140.00$.

What is a straight commission?

A compensation model in which an employee earns a single, fixed percentage on all sales made, regardless of the sales volume.

If Marvin earns a $5\%$ straight commission on product sales, how much will he receive for selling $\text{Php } 50,000$ worth of products?

$$\text{Commission} = 0.05 \times \text{Php } 50,000 = \text{Php } 2,500.00$$

What is a graduated or tiered commission?

A commission structure in which an employee earns increasing commission percentage rates as sales reach different specified levels or brackets.

Francis earns $3\%$ on the first $\text{Php } 50,000$, $4\%$ on the next $\text{Php } 50,000$, and $5\%$ on sales over $\text{Php } 100,000$. What is his total commission on $\text{Php } 160,000$ of sales?

First bracket: $50,000 \times 0.03 = \text{Php } 1,500.00$. Second bracket: $50,000 \times 0.04 = \text{Php } 2,000.00$. Over bracket: $(160,000 - 100,000) \times 0.05 = 60,000 \times 0.05 = \text{Php } 3,000.00$. Total commission is $1,500 + 2,000 + 3,000 = \text{Php } 6,500.00$.

How is a salary plus commission plan defined?

An arrangement where an employee receives a guaranteed fixed base salary plus an additional commission based on sales volume.

Josie has a monthly base salary of $\text{Php } 18,000$ and earns a $6\%$ commission. If she sells $\text{Php } 150,000$ worth of goods, what are her total monthly earnings?

Her commission is $0.06 \times 150,000 = \text{Php } 9,000.00$. Total earnings are $18,000 + 9,000 = \text{Php } 27,000.00$.

What is a draw against commission?

A pay plan where an employee is given a regular cash advance (draw) against anticipated future commissions, which is then subtracted from the commissions actually earned.

Mr. Fernando receives a monthly draw of $\text{Php } 20,000$ and a $5\%$ commission on sales. If he sells $\text{Php } 350,000$ in a month, how much does he receive?

Commission earned is $0.05 \times 350,000 = \text{Php } 17,500.00$. Subtracting the draw yields $17,500 - 20,000 = -\text{Php } 2,500.00$. He receives nothing that month and owes $\text{Php } 2,500.00$ to the company.

What is an override commission?

A commission earned by a manager or supervisor calculated as a percentage of the sales or commissions achieved by the sales representatives under their supervision.

How does inflation affect the purchasing power of consumers?

Inflation is the rate of increase in the prices of goods or services; as prices rise, the purchasing power of money decreases, meaning a specific amount of money buys fewer goods and services.

What is the difference between nominal wage and real wage?

Nominal wage is the face-value monetary compensation received without adjusting for inflation, while real wage is compensation adjusted for inflation, reflecting the true purchasing power of the earnings.

What is the formula for calculating the Consumer Price Index (CPI)?

$$\text{CPI} = \frac{\text{Cost of Market Basket in Current Period}}{\text{Cost of Market Basket in Previous Period}} \times 100$$

What is always the numerical value of the Consumer Price Index (CPI) in the base year?

The CPI for the base year is always $100$.

If a selected market basket cost $\text{P}4,350$ in the 2018 base year and $\text{P}5,775$ in 2024, what is the CPI for 2024?

$$\text{CPI} = \frac{5,775}{4,350} \times 100 = 1.3276 \times 100 = 132.76$$

What does a Consumer Price Index (CPI) of $132.76$ indicate relative to the base year?

It indicates that the average price of that basket of goods has increased by approximately $32.76\%$ compared to the base year.

What formula calculates the inflation rate between two periods using CPI?

$$\text{Inflation Rate} = \frac{\text{Current CPI} - \text{Previous CPI}}{\text{Previous CPI}} \times 100$$

If the CPI in 2024 is $132.76\%$ and the CPI in 2023 was $127.3\%$, what is the annual inflation rate?

$$\text{Inflation Rate} = \frac{132.76 - 127.3}{127.3} \times 100 = \frac{5.46}{127.3} \times 100 = 4.29\%$$

What is the general formula for percentage change in prices or wages?

$$\text{Percentage Change} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100$$

If the price of meat increases from $\text{P}280$ to $\text{P}350$ per kilogram, what is the percentage increase?

$$\text{Percentage Increase} = \frac{350 - 280}{280} \times 100 = \frac{70}{280} \times 100 = 25\%$$

Fernando's salary increased from $\text{P}22,000$ to $\text{P}23,800$. If inflation during the period was $9\%$, what happened to his real wage?

His nominal salary increased by $\frac{23,800 - 22,000}{22,000} \times 100 = 8.18\%$. Because the $8.18\%$ salary increase is less than the $9\%$ inflation rate, his real wage decreased.

How is a markup defined in commercial transactions?

A markup is the difference between the selling price and the cost price ($\text{Markup} = \text{Selling Price} - \text{Cost Price}$), representing the amount added to the acquisition cost to generate profit.

What formula calculates the markup rate based on cost price?

$$\text{Markup Rate} = \frac{\text{Markup}}{\text{Cost Price}} \times 100$$

A merchant buys a product for $\text{P}2,500$ and sells it for $\text{P}2,990$. What is the markup rate?

The markup is $2,990 - 2,500 = \text{P}490$. The markup rate is $\frac{490}{2,500} \times 100 = 19.6\%$.

An appliance seller purchases a washing machine for $\text{P}8,500$ and applies an $8\%$ markup rate. What is the selling price?

$$\text{Selling Price} = \text{Cost Price}(1 + \text{Markup Rate}) = 8,500 \times (1 + 0.08) = 8,500 + 680 = \text{P}9,180$$

What is a discount, and how is the discount amount computed from the list price?

A discount is a reduction subtracted from the original list price to encourage sales; its amount is calculated as $\text{Discount} = \text{List Price}(\text{Discount Rate})$.

What is the net price, and what formula expresses it in terms of list price and discount rate?

Net price is the final amount paid after deducting the discount: $\text{Net Price} = \text{List Price} - \text{Discount} = \text{List Price}(1 - \text{Discount Rate})$.

An electronic gadget with a list price of $\text{P}12,600$ is sold with a $15\%$ discount. What are the discount amount and net price?

The discount is $12,600 \times 0.15 = \text{P}1,890$, and the net price is $12,600 - 1,890 = \text{P}10,710$.

A laptop originally priced at $\text{P}38,000$ is sold for $\text{P}34,500$. What is the discount rate?

The discount is $38,000 - 34,500 = \text{P}3,500$. The discount rate is $\frac{3,500}{38,000} \times 100 \approx 9.21\%$.

A pair of leather shoes is sold for $\text{P}2,800$. If the store applied a $12\%$ markup on cost, what is the cost price?

$$\text{Cost Price} = \frac{\text{Selling Price}}{1 + \text{Markup Rate}} = \frac{2,800}{1 + 0.12} = \frac{2,800}{1.12} = \text{P}2,500$$

How does the Philippines' Bureau of Internal Revenue (BIR) define Value-Added Tax (VAT)?

VAT is an indirect tax on consumption imposed on the sale, barter, exchange, or lease of goods, properties, and services in the Philippines, as well as on imports, which may be shifted or passed on to the buyer.

What is the standard VAT rate in the Philippines, and what annual sales threshold mandates VAT registration?

The tax rate is twelve percent ($12\%$), and businesses with gross annual sales exceeding $\text{P}3,000,000$ are required to register and collect VAT.

What formulas give the VAT amount ($V$) and VAT-inclusive price ($V_i$) when the VAT-exclusive price ($V_e$) is known?

$V = 0.12(V_e)$ and $V_i = V_e + V = 1.12(V_e)$.

What formulas compute the VAT-exclusive price ($V_e$) and VAT amount ($V$) from a VAT-inclusive price ($V_i$)?

$V_e = \frac{V_i}{1.12}$ and $V = \frac{0.12}{1.12} V_i$.

A product sells for $\text{P}30,000$ exclusive of VAT. What are the VAT amount and the VAT-inclusive price?

The VAT amount is $0.12 \times 30,000 = \text{P}3,600$, and the VAT-inclusive price is $1.12 \times 30,000 = \text{P}33,600$.

A LED TV has a VAT-inclusive price of $\text{P}21,580$. What are the VAT amount and the VAT-exclusive price?

The VAT amount is $\frac{0.12}{1.12} \times 21,580 = \text{P}2,312.14$, and the VAT-exclusive price is $\frac{21,580}{1.12} = \text{P}19,267.86$.