The annual grain procurement of a regional warehouse over three consecutive years grew from $40\text{ lakh tonnes}$ in 2021 to $75\text{ lakh tonnes}$ in 2024. The compound annual growth rate (CAGR) in percentage over this 3-year period is ________ % (round off to 2 decimal places).
Answer Key:
23.31
Step-by-Step Solution & Explanation
1. Initial value $V_0 = 40$, final value $V_3 = 75$, time period $n = 3\text{ years}$.
2. CAGR formula:
$\text{CAGR} = \left(\frac{V_n}{V_0}\right)^{1/n} - 1 = \left(\frac{75}{40}\right)^{1/3} - 1 = (1.875)^{1/3} - 1$
3. Calculation:
$(1.875)^{1/3} \approx 1.233106$
$\text{CAGR} = 1.233106 - 1 = 0.233106 = 23.31\%$