Chapter 3
Nested Percentages
Percentage of a percentage, multi-level hierarchical calculations
3.1 What is a nested percentage?
A nested percentage is a percentage applied to the result of another percentage, not to the original total.
Level 0 (total) × rate_1 = Level 1 Level 1 × rate_2 = Level 2 Final value = Total × rate_1 × rate_2 × ...
💡 Common error: applying the inner percentage to the grand total instead of to the intermediate result.
3.2 Chaining multiple levels
Final value = Total × rate_1 × rate_2 × rate_3
Example: budget €900 000. Administration = 35%, within that IT = 20%, within IT hardware = 60%. Hardware = 900 000 × 0.35 × 0.20 × 0.60 = €37 800.
3.3 Multi-group problems
Group result = Total_group × rate_A × rate_B Grand total = sum of all group results
Example: Factory A: 400 × 80% × 30% = 96 units. Factory B: 600 × 65% × 45% = 175.5 units. Factory C: 350 × 90% × 50% = 157.5 units. Total = 429 units.