Real Estate Mathematics: Area, Percentages, and Direct Capitalization.

1. Area Calculation

• Regular Areas:
  • Square: Area = Length x Width (Area = L x W). Since Length = Width, Area = L². Example: Square with side 10 meters, area = 10 x 10 = 100 square meters.
  • Rectangle: Area = Length x Width (Area = L x W). Example: Rectangle with length 15 meters and width 8 meters, area = 15 x 8 = 120 square meters.
  • Triangle: Area = (Base x Height) / 2 (Area = (B x H) / 2). Example: Triangle with base 12 meters and height 7 meters, area = (12 x 7) / 2 = 42 square meters.
  • Circle: Area = π x (radius)² (Area = πr²) where π ≈ 3.14. Example: Circle with radius 5 meters, area = 3.14 x (5)² = 78.5 square meters.

• Irregular Areas: Divide into smaller regular shapes, calculate each area, and sum them. Example: An irregular plot divided into a square (S), rectangle (R), and triangle (T).

  1. Area (S) = L x W = 40 ft x 40 ft = 1600 sq ft.
  2. Area (R) = L x W = 30 ft x 25 ft = 750 sq ft.
  3. Area (T) = (B x H) / 2 = (30 ft x 30 ft) / 2 = 450 sq ft.
  4. Total Area = 1600 + 750 + 450 = 2800 sq ft.

• Volume Calculation:

  • Cube/Rectangular Prism: Volume = Length x Width x Height (Volume = L x W x H). Example: Room with dimensions 15 ft x 10 ft x 10 ft, volume = 15 x 10 x 10 = 1500 cubic feet.

2. Percentages

• Percentage means “per hundred”. Express any number as a percentage by multiplying by 100 and adding “%”.
• Percentage to Decimal: Divide by 100. Example: 8.5% = 8.5 / 100 = 0.085.
• Decimal to Percentage: Multiply by 100 and add “%”. Example: 0.095 = 0.095 x 100 = 9.5%.
• Part, Whole, and Percentage:
  • Part = Percentage x Whole
  • Percentage = Part / Whole
  • Whole = Part / Percentage
• Examples:
  • House (1500 sq ft) on a lot (7500 sq ft): Percentage = (1500 / 7500) x 100 = 20%.
  • Property value ($500,000) increases by 5% annually: Increase = 0.05 x $500,000 = $25,000.

3. Direct Capitalization

• Estimates property value based on income.
• Net Operating Income (NOI): Income after operating expenses (taxes, insurance, maintenance, management) but before debt payments.
• Capitalization Rate (Cap Rate): Ratio of NOI to property value, reflecting expected return on investment.
• Property Value (Value): Estimated value based on income and cap rate.
• IRV Formula: Income = Rate x Value
  • Rate = Income / Value
  • Value = Income / Rate
• Example: Property with $40,000 annual income, 25% cap rate: Value = $40,000 / 0.25 = $160,000.
• Income Multiplier: Reciprocal of cap rate. Income Multiplier = 1 / Cap Rate. In the previous example, Income Multiplier = 1 / 0.25 = 4.

4. Interest

• Simple Interest: Calculated only on the principal.
  • Interest = Principal x Rate x Time
  • Principal: Original investment/loan amount.
  • Rate: Annual interest rate.
  • Time: Duration of interest calculation (usually in years).
• Example: $1000 investment at 12% annually for 6 months: Interest = $1000 x 0.12 x (6/12) = $60.
• Other Calculations:
  • Principal = Interest / (Rate x Time)
  • Rate = Interest / (Principal x Time)
  • Time = Interest / (Principal x Rate)