Mathematical Formula For Calculating Percentage Rate Growth
\[ \text{Growth Rate} = \left( \left( \frac{\text{Final Value}}{\text{Initial Value}} \right)^{\frac{1}{\text{Time Period}}} – 1 \right) \times 100 \]
Example Broken Down With Steps
$$
\text{Given: Initial Value = 100, Final Value = 200, Years = 3}
$$
$$
\text{Step 1: Divide final value by initial value: } \frac{200}{100} = 2
$$
$$
\text{Step 2: Take the cube root: } \sqrt[3]{2} = 1.2599
$$
$$
\text{Step 3: Subtract 1: } 1.2599 – 1 = 0.2599
$$
$$
\text{Step 4: Multiply by 100: } 0.2599 \times 100 = 25.99
$$
$$
\text{Result: Annual Growth Rate is 25.99%.}
$$
Further Explained
Example: A value grew from 100 to 200 over 3 years.
Steps:
- Divide the final value by the initial value:
$$ \frac{200}{100} = 2 $$ - Take the cube root (since it spans 3 years):
$$ \sqrt[3]{2} = 1.2599 $$ - Subtract 1:
$$ 1.2599 – 1 = 0.2599 $$ - Multiply by 100:
$$ 0.2599 \times 100 = 25.99 $$ - Conclusion: The annual growth rate is 25.99%.