02 // Visual Math & Finance SolversΔ% = [(V_new − V_old) / V_old] × 100%
Visual Percentage Change, Increase & Asymmetry Explorer
Percentage change measures relative delta from an initial reference $V_0$ as $\Delta\% = \frac{V_1 - V_0}{|V_0|} \times 100\%$; sequential percentage changes multiply as $(1 + r_1)(1 - r_2)$ rather than adding linearly.
Δ% = [(V_new − V_old) / V_old] × 100%Inputs & Parameters (3)
$
50$±5010000$
%
0%±1100%
%
0%±195%
25% of $1,000
$250
Remainder = $750 (75%)
Increased (+25%)
$1,250
Multiplier = 1.250×
Discounted (−25%) + 20%
$900
Net factor = 90.00% of base
Recovery Gain Needed
+33.33%
To recover from a −25% drawdown
20-Row Comparison Table
Compare across:
| # | Starting Reference Value (V₀) ($) | Primary Share (P₁% of V) | V × (1 − 25%) | With +20% Tax |
|---|---|---|---|---|
| 01 | 50 $ | $12.50 | $37.50 | $45.00 |
| 02 | 550 $ | $138 | $413 | $495 |
| 03 | 1,100 $ | $275 | $825 | $990 |
| 04 | 1,600 $ | $400 | $1,200 | $1,440 |
| 05 | 2,150 $ | $538 | $1,613 | $1,935 |
| 06 | 2,650 $ | $663 | $1,988 | $2,385 |
| 07 | 3,200 $ | $800 | $2,400 | $2,880 |
| 08 | 3,700 $ | $925 | $2,775 | $3,330 |
| 09 | 4,250 $ | $1,063 | $3,188 | $3,825 |
| 10 | 4,750 $ | $1,188 | $3,563 | $4,275 |
| 11 | 5,300 $ | $1,325 | $3,975 | $4,770 |
| 12 | 5,800 $ | $1,450 | $4,350 | $5,220 |
| 13 | 6,350 $ | $1,588 | $4,763 | $5,715 |
| 14 | 6,850 $ | $1,713 | $5,138 | $6,165 |
| 15 | 7,400 $ | $1,850 | $5,550 | $6,660 |
| 16 | 7,900 $ | $1,975 | $5,925 | $7,110 |
| 17 | 8,450 $ | $2,113 | $6,338 | $7,605 |
| 18 | 8,950 $ | $2,238 | $6,713 | $8,055 |
| 19 | 9,500 $ | $2,375 | $7,125 | $8,550 |
| 20 | 10,000 $ | $2,500 | $7,500 | $9,000 |
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Key Analytical Takeaways
- 01A $+25\%$ gain followed by a $-20\%$ loss returns exactly to $1.00\times$ ($1.25 \times 0.80 = 1.00$), demonstrating base-shift asymmetry.
- 02In general, recovering from a $-L\%$ drawdown requires a $+\frac{L}{100 - L} \times 100\%$ gain.
- 03The difference between two percentages is measured in 'percentage points' (pp), whereas their relative shift is 'percent change'.
Frequently Asked Questions
Why doesn't a 20% increase followed by a 20% decrease bring you back to the original number?+
Because the 20% decrease is taken from the larger, already-increased number: 1.20 × 0.80 = 0.96, leaving you 4% below your starting point.
What is the difference between percent change and percentage points?+
Moving from 10% to 15% is an increase of 5 percentage points, but a 50% relative increase ((15 - 10) / 10 = 50%).
What is the difference between percentage change and percentage point change?+
Moving an interest rate from 4% to 6% is an increase of 2 percentage points (additive difference), which corresponds to a 50% relative percentage increase ((6 − 4) / 4 = 0.50).