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Calculate compound percentage changes over multiple periods. See how percentages compound and compare to simple percentage growth.
Use negative values for decreases
Each period's change is applied to the previous period's result, not the original value. This creates exponential growth (or decay) rather than linear.
Enter values to calculate compound percentage
Example: $100 growing at 10% for 3 periods = $100 × (1.10)³ = $133.10
With compounding, each period's growth builds on the previous period's total, not just the original amount.
Simple: Same absolute amount added each period
Compound: Percentage of current value added each period
The difference grows larger over time - this is why compound interest is powerful!
Compound percentage means each period's percentage change applies to the current value (including previous changes), not the original value. This creates exponential growth or decay. It's different from simple percentage where the same amount is added each period.
Use the formula: Final = Initial × (1 + rate/100)^periods. For example, $1000 growing 5% annually for 3 years: $1000 × (1.05)³ = $1,157.63. The exponent is key - it represents repeated multiplication.
Simple percentage applies the rate to the original value each time (linear growth). Compound applies it to the current value (exponential growth). For 10% on $100 over 3 periods: Simple = $130, Compound = $133.10. The difference grows over time.
Yes! Negative compound percentages represent decay. For example, -5% compounded over 3 periods on $100: $100 × (0.95)³ = $85.74. Each period you lose 5% of what remains, not 5% of the original.
Common uses: compound interest on savings/loans, investment returns, inflation, population growth, radioactive decay, viral spread, depreciation of assets, and any situation where growth builds on itself.
If you know initial and final values: Rate = ((Final/Initial)^(1/periods) - 1) × 100. For example, if $100 became $133.10 in 3 periods: Rate = ((133.10/100)^(1/3) - 1) × 100 = 10%.
A quick way to estimate compound growth: divide 72 by the growth rate to find how many periods it takes to double. At 6% growth, 72/6 = 12 periods to double. It's surprisingly accurate for typical rates!
More frequent compounding means more growth. 12% annually = 12% once. 12% compounded monthly = (1.01)¹² = 12.68% effectively. More periods at smaller rates beats fewer periods at higher rates due to exponential growth.