Step 1: Understanding the Concept:
The Compound Annual Growth Rate (CAGR) measures the average annual growth of an investment over a period exceeding one year. It signifies the consistent rate at which an investment would have grown, assuming annual compounding.
Step 2: Key Formula or Approach:
The CAGR is calculated using the following formula:\[ \text{CAGR} = \left( \frac{\text{Ending Value}}{\text{Beginning Value}} \right)^{1/n} - 1 \]In this formula:- Ending Value represents the investment's value at the conclusion of the period.- Beginning Value represents the investment's value at the inception of the period.- \(n\) denotes the duration in years.
Step 3: Detailed Explanation:
From the problem statement:- Beginning Value = Rupees 10,000 (initial investment)- Ending Value = Rupees 14,000 (value at the end of 2023)- Number of years (\(n\)) = 6 years (investment holding period)
Substitute these values into the CAGR formula:\[ \text{CAGR} = \left( \frac{14,000}{10,000} \right)^{1/6} - 1 \]\[ \text{CAGR} = (1.4)^{1/6} - 1 \]Given that \((1.4)^{1/6} \approx 1.058\).\[ \text{CAGR} \approx 1.058 - 1 = 0.058 \]To express this as a percentage, multiply by 100:\[ \text{CAGR} = 0.058 \times 100% = 5.8% \]Step 4: Final Answer:
The compound annual growth rate (CAGR) for the investment is 5.8%.