Encyclopedic Study Guide on General Mathematics: Compensation, Business Math, and Sequences

SALARY AND WAGES COMPENSATION

• Definition: Remuneration given to an employee in exchange for his or her services.

• Salary: Refers to a fixed regular wage. It is typically paid on a monthly, semi-monthly, or weekly basis.

  • Annual Salary: The total amount of money a person earns in one year.

  • Monthly Salary: The fixed amount an employee earns every month.

• Wage: The remuneration or earnings, however designated, capable of being expressed in terms of money. It is fixed or ascertained on a time, task, piece, or commission basis.

  • Daily Wage: The amount of money a worker earns for each day of actual work.

  • Hourly Wage: The amount earned for each hour worked.

SALARY AND WAGE COMPUTATION FORMULAS

• Standard Wage Computations:

  • $Wage = (\text{hourly rate}) \times (\text{no. of hours worked})$

  • $Wage = (\text{daily rate}) \times (\text{no. of days worked})$

  • $\text{Daily Rate} = \frac{\text{Monthly Salary}}{\text{No. of days worked}}$

  • $\text{Hourly Rate} = \frac{\text{Daily Rate}}{8\,\text{hours}}$

ADDITIONAL COMPENSATIONS: OVERTIME AND HOLIDAY PAY

• ART. 86. Overtime Work: Work may be performed beyond eight (8) hours a day provided that the employee is paid for the overtime work an additional compensation equivalent to his regular wage plus at least twenty-five percent (25%) thereof.

• ART. 87. Premium and Overtime Pay for Holiday and Rest Day Work: Any employee performing work on holidays or on his scheduled rest days, not exceeding eight (8) hours, shall be paid an additional compensation of not less than thirty percent (30%) of his regular wage.

  • Excess Work on Holidays/Rest Days: For work performed in excess of eight (8) hours on such days, the employee shall be paid an additional compensation equivalent to his rate for the first eight (8) hours on a holiday or rest day plus at least thirty percent (30%) thereof.

• Specific Rate Calculations:

  • Overtime Pay: $(\text{OT Hours}) \times (\text{Hourly Rate}) \times 1.25$

  • Work on a Rest Day or Special Holiday: $(\text{Daily Rate}) \times 1.30$

  • Work on a Regular Holiday: $(\text{Daily Rate}) \times 2.00$

  • Work on a Regular Holiday falling on a Rest Day: $(\text{Daily Rate}) \times 2.60$

  • Night Shift Differential: Applicable for work between 10PM and 6AM. Multiply the applicable rate by $1.10$.

COMMISSION AND PIECEWORK EARNINGS

• Commission Income: Earned as a percentage of sales made. It can be pure commission or a base salary plus commission.

  • $\text{Commission} = (\text{Total Sales}) \times (\text{Commission Percentage})$

• Piecework Earnings: Based on the number of items or products completed.

  • Straight Piece Rate: $\text{Wage} = (\text{Quantity}) \times (\text{Rate})$

  • Graduated Piece Rate: $\text{Wage} = Q_1 R_1 + Q_2 R_2 + \dots + Q_n R_n$

  • Notation: $Q_1, Q_2, \dots, Q_n$ represent quantities produced by interval; $R_1, R_2, \dots, R_n$ represent corresponding rates for those intervals.

BENEFITS AND DEDUCTIONS

• Taxable Benefits: Benefits an employer must add to an income to determine the total amount subject to tax. Examples: salary, wage, commissions, dividends, investment income, royalties, honorarium.

• Nontaxable Benefits:

  • Monetized unused vacation leave (private employees): Not exceeding 10 days/year.

  • Monetized vacation and sick leave (government employees).

  • Uniform and clothing allowance: Not exceeding $\text{₱4,000}$ per annum.

  • Christmas gift: Not exceeding $\text{₱5,000}$ per annum.

  • Medical cash allowance: Not exceeding $\text{₱750.00}$ per employee.

• Standard Employee Benefits:

  • Vacation Leave: 13 vacation days, with one additional day added starting on the second year of service.

  • Sick Leave: 12 days with pay for the first two years of service.

  • 13th Month Pay: One-twelfth ($\frac{1}{12}$) of the annual salary or wage; nontaxable if below $\text{₱80,000}$.

  • Other Benefits: Bonuses, clothing/housing allowances, medical insurance.

MANDATORY DEDUCTIONS AND CONTRIBUTIONS

• Social Security System (SSS): Mandated for private employees by Republic Act No. 11199 (Social Security Act of 2018).

  • Total Monthly Contribution Rate: $15\%$ of the salary.

  • Split: Employer (ER) = $10\%$, Employee (EE) = $5\%$.

  • MSC (Monthly Salary Credit): A rounded salary value used as a basis for computing contributions.

  • EC: Additional fixed amount paid only by the employer for work-related sickness/injury.

  • MPF: Long-term savings or investment fund managed by SSS.

• Government Service Insurance System (GSIS): Mandated for government employees under RA 8291.

  • Employee Share: $9\%$ of monthly salary.

  • Employer Share: $12\%$ of monthly salary.

  • $\text{GSIS contribution} = (\text{Monthly Salary}) \times 0.09$

• PhilHealth: Mandated by RA 11223 (Universal Health Care Act).

  • Premium Rate (Effective Jan 2025): $5.0\%$

  • Income Floor: $\text{₱10,000}$

  • Income Ceiling: $\text{₱100,000}$

  • $\text{PhilHealth} = (\text{Monthly Salary}) \times 0.025$

• Pag-IBIG Fund (HDMF): Home Development Mutual Fund.

  • Contribution Ceiling: Shares for both employee and employer are capped at $\text{₱200}$ each.

• Withholding Tax: Tax withheld from income payments arising from employer-employee relationships.

• Voluntary Deductions: Optional deductions like salary loans, insurance premiums, union dues, or cooperative dues.

NET PAY COMPUTATION STEPS

• Step 1: Solve for Gross Income.

• Step 2: Subtract Non-Taxable Deductions.

• Step 3: Compute Income Tax (refer to BIR table).

• Final Formula:

  • $\text{Net Pay} (NP) = \text{Gross Pay} (GP) - \text{Deductions} (D)$

  • $\text{Net Pay} = GP - (\text{SSS/GSIS} + \text{PhilHealth} + \text{Pag-IBIG} + \text{Tax})$

INFLATION AND PERCENTAGE CHANGES

• Percentage Changes:

  • Positive Result: Indicates a percentage increase.

  • Negative Result: Indicates a percentage decrease.

• Percentage Increase: New value > Original value. Found by determining the amount of increase as a percentage of the original value.

• Percentage Decrease: New value < Original value. Found by determining the amount of decrease as a percentage of the original value (original value is always the denominator).

• Inflation: General increase in prices of goods and services over time leading to decreased purchasing power.

• Causes of Inflation:

  1. Demand-pull Inflation: Demand exceeds production capacity, causing prices to rise.

  2. Cost-push Inflation: Prices increase due to higher production costs (raw materials/wages).

  3. Built-in Inflation: Price-wage spiral where businesses raise prices to offset rising wages.

MARK-UP, VAT, AND PROFIT/LOSS

• Mark-Up: Amount added to the cost price to ensure profit.

  • $\text{Markup} = \text{Cost Price} \times \text{Markup Rate}$

  • $\text{Selling Price} = \text{Cost Price} + \text{Markup}$

• Value Added Tax (VAT): Sales tax on goods/services in the Philippines (Standard rate = $12\%$).

  • VAT Exempted: Educational services, Books/Newspapers, Senior Citizen/PWD purchases, Residential houses, Agricultural/Food products.

  • $\text{VAT} = \text{Base Price} \times 0.12$

  • $\text{Total Payment} = \text{Base Price} \times (1 + 0.12)$

• Business Terms:

  • Cost Price (CP): Total expenses incurred in acquiring or producing an item.

  • Selling Price (SP): Price at which the business sells the item to a customer.

  • Revenue: Money earned before deducting costs.

  • Profit: High selling price vs. cost price (SP > CP). $\text{Profit} = SP - CP$

  • Loss: High cost price vs. selling price (SP < CP). $\text{Loss} = CP - SP$

PATTERNS AND SEQUENCES

• Pattern: Repeated or predictable arrangement of elements following a rule.

  • Art: Repetition of lines, shapes, and colors for rhythm.

  • Nature: Natural shapes/lines in plants and animals.

  • Spiral: Curve moving outward from a central point.

  • Fibonacci: Series where each number is the sum of the two preceding numbers.

• Sequence: Ordered list of numbers following a specific rule.

  • Term: Each number in a sequence (e.g., in $3, 6, 12, 24$, $3$ is the 1st term).

  • Position: The index or place (1st, 2nd, etc.).

  • Notation: $a_1 = \text{1st term}$, $a_2 = \text{2nd term}$, $a_n = \text{nth/general term}$.

  • Finite Sequence: Has a specific start and end (e.g., $2, 4, 6, 8, 10$).

  • Infinite Sequence: Continues forever ($\dots$) (e.g., $1, 2, 3, 4, 5, \dots$).

ARITHMETIC AND GEOMETRIC SEQUENCES

• Arithmetic Sequences: Terms obtained by adding a constant number called the common difference ($d$).

  • $d = a_n - a_{n-1}$

  • Examples: $5, 9, 13, 17 \rightarrow d=4$; $20, 18, 16 \rightarrow d=-2$.

• Geometric Sequences: Terms obtained by multiplying the preceding term by a fixed non-zero number called the common ratio ($r$).

  • Examples: $2, 4, 8, 16 \rightarrow r=2$; $81, 27, 9 \rightarrow r=\frac{1}{3}$; $1, -2, 4, -8 \rightarrow r=-2$.