Inflation

Fundamentals of Inflation and Price Adjustments

  • Definition of Inflation:

    • Inflation is defined as the continuous increase in the prices of goods and services over time.
    • As price levels rise, the purchasing power of money decreases.

  • Formulas for Inflation Calculations:

    • Price Increase Formula:     Increase=Original Price×Rate of Increase\text{Increase} = \text{Original Price} \times \text{Rate of Increase}
    • New Price Formula:     New Price=Original Price+Increase\text{New Price} = \text{Original Price} + \text{Increase}

  • Step-by-Step Worked Example: Price Increase of Rice:

    • Initial Conditions: Last year, a kilogram of rice cost P 50P\,50. This year, due to inflation, the price increased by 10%10\% (0.100.10).
    • Step 1: Calculate the Amount of Increase:     Increase=50×10%\text{Increase} = 50 \times 10\%Increase=50×0.10\text{Increase} = 50 \times 0.10Increase=P 5\text{Increase} = P\,5
    • Step 2: Add the Increase to the Original Price:     P=50+5P = 50 + 5P=P 55P = P\,55
    • Final Price: The new price of the rice after inflation is P 55P\,55.

Business Mathematics: Mark-Up and Selling Price

  • Definition of Mark-Up:

    • A mark-up is defined as the amount added to the cost price of a product to determine its final selling price.

  • Formulas for Mark-Up Calculations:

    • Mark-Up Amount Formula:     Mark-Up Amount=Cost Price×Mark-Up Rate\text{Mark-Up Amount} = \text{Cost Price} \times \text{Mark-Up Rate}
    • Selling Price Formula:     Selling Price=Cost Price+Mark-Up Amount\text{Selling Price} = \text{Cost Price} + \text{Mark-Up Amount}

  • Step-by-Step Worked Example: Calculating Mark-Up on a Backpack:

    • Initial Conditions: A store bought a backpack (problem statement references buying for 300300 with a 20%20\% mark-up, while the detailed solution calculates based on a cost price of 800800 with a 25%25\% mark-up rate).
    • Step 1: Find the Mark-Up Amount:     P=800×25%P = 800 \times 25\%P=800×0.25P = 800 \times 0.25P=200P = 200
    • Step 2: Find the Selling Price:     P=800+200P = 800 + 200P=P 1000P = P\,1000
    • Final Result: The selling price of the backpack is 10001000 (or P 1000P\,1000).

Consumer Mathematics: Discount and Sale Price

  • Definition of Discount:

    • A discount is defined as a reduction from the original price of an item.

  • Formulas for Discount Calculations:

    • Discount Amount Formula:     Discount Amount=Original Price×Discount Rate\text{Discount Amount} = \text{Original Price} \times \text{Discount Rate}
    • Sale Price Formula:     Sale Price=Original Price−Discount Amount\text{Sale Price} = \text{Original Price} - \text{Discount Amount}

  • Step-by-Step Worked Example: Calculating Discount on a Jacket:

    • Initial Conditions: A jacket costs $2,000\$2{,}000 (or P 2,000P\,2{,}000) and is offered at a 15%15\% discount (0.150.15).
    • Step 1: Find the Discount Amount:     P=2,000×15%P = 2{,}000 \times 15\%P=2,000×0.15P = 2{,}000 \times 0.15P=300P = 300
    • Step 2: Find the Sale Price:     Sale Price=$2,000−300\text{Sale Price} = \$2{,}000 - 300Sale Price=P 700\text{Sale Price} = P\,700
    • Final Result: The final sale price of the jacket is P 700P\,700.