Percent is a fraction wearing a suit: x% = x/100. So 8% of ₹6,25,000 = 0.08 × 6,25,000 = ₹50,000. Always convert to a decimal before computing. Most percentage errors are misplaced decimal points.
How do you calculate percentage change?
Percentage change compares a new level to an old one:
% change = (New − Old) / Old
A share moving from ₹480 to ₹552 changed by 72/480 = 0.15 = +15%. The denominator is the starting value, and that creates a famous asymmetry.
Losses and gains aren't symmetric. Fall 20% and then rise 20%, and ₹100 becomes ₹80 and then ₹96. You're down 4%, because the 20% rise acted on the smaller base. In general, after a loss of L written as a decimal, the gain you need to recover is L / (1 − L):
| Fall | Gain needed to recover |
|---|---|
| −10% | +11.1% |
| −25% | +33.3% |
| −50% | +100% |
| −60% | +150% |
| −90% | +900% |
This one table explains half of risk management. A portfolio that avoids the −50% year has a structurally easier life than one that must find a +100% year. Keep it somewhere you'll see it, because Phase 9 builds on it.
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What is the difference between percentage points and percent?
Percentage points (pp) versus percent. When a ratio changes, describe the change in points, or you'll create the kind of ambiguity real analysts get burned by. A company's EBIT margin moving from 18.0% to 21.5% rose 3.5 percentage points, which is a 19.4% relative increase (3.5/18.0). "Margin rose 19%" and "margin rose to 21.5%" are different claims. Sloppy writers blur them. Careful analysts never do.
Basis points (bp). One basis point is one-hundredth of a percentage point: 1 bp = 0.01% = 0.0001. So 100 bp = 1%, and 25 bp = 0.25%. Rates, spreads, fees and margin moves are quoted in bp to kill the pp/percent ambiguity. When the RBI or the Fed moves its policy rate, the announcement says "25 basis points," never "0.25 percent," and a mutual fund expense ratio of 0.45% is "45 bp." Make two conversions automatic. One is bp → decimal: divide by 10,000, so 40 bp = 0.0040. Its reverse is decimal → bp: multiply by 10,000, so 0.0007 = 7 bp. On ₹2 crore, 40 bp = 0.0040 × 2,00,00,000 = ₹80,000. Small-sounding units, then, but real money.
How do growth rates work over several periods?
Next comes the multiplication habit. To grow by rate g, multiply by the growth factor (1 + g). To apply several periods of growth, multiply the factors:
Total growth = (1 + g₁)(1 + g₂)…(1 + gₙ) − 1
Take revenue growing +25%, +18%, −7% over three years. It ends at 1.25 × 1.18 × 0.93 = 1.37175, a total of +37.2%. Never add growth rates across periods. Adding gives 25 + 18 − 7 = 36, which is wrong, and the error grows with size and time. The average annual pace of that three-year run isn't (25 + 18 − 7)/3 = 12% either. It's the rate that, compounded three times, gives 1.37175: 1.37175^(1/3) − 1 = 11.11%. That number has a name, and you'll meet it in a moment (see CAGR).
The deceleration trap comes from mixing up a growth rate with a level. "Inflation fell from 6% to 4%" means prices are still rising, just more slowly. "Revenue growth decelerated from 24% to 12%" means revenue hit a new all-time high at a slower pace. The rate is the slope and the level is the altitude, and a falling slope doesn't mean a falling altitude. Newspapers, managements and beginners mix the two up constantly, reading "India's GDP growth is slowing" as if it said "India's GDP is shrinking". There's a subtler second layer too. When growth halves from 24% to 12%, this year's absolute addition is 0.12 × 1.24 = 0.149 of the old base. That's smaller than last year's 0.24, even though the base grew. Check the arithmetic before you assume either direction.