Question

A person invested Rupees 10000 in a stock of a company for 6 years. The value of his investment at the end of each year is given in the following table:
\begin{tabular}{|c|c|c|c|c|c|} \hline 2018 & 2019 & 2020 & 2021 & 2022 & 2023
\hline Rupees 11000 & Rupees 11500 & Rupees 13000 & Rupees 11800 & Rupees 12200 & Rupees 14000
\hline \end{tabular}
The compound annual growth rate (CAGR) of his investment is:
Given \((1.4)^{1/6} \approx 1.058\)

• A. 5.8%
• B. 4.2%
• C. 6.8%
• D. 3.2%

Hint:

CAGR is a smoothing metric. Notice that the investment value fluctuates year to year (it even decreased in 2021). CAGR ignores this volatility and provides a single, representative growth rate over the entire period. It only considers the starting and ending values.

Answer 1

The Correct Option is A

Step 1: Concept Definition:
The Compound Annual Growth Rate (CAGR) measures the average annual growth of an investment over a period exceeding one year. It indicates the consistent rate at which an investment would have grown annually if it compounded uniformly.

Step 2: Calculation Formula:
The CAGR is calculated using the following formula:
\[ \text{CAGR} = \left( \frac{\text{Ending Value}}{\text{Beginning Value}} \right)^{1/n} - 1 \]
Where:
- Ending Value: The investment's value at the end of the period.
- Beginning Value: The investment's value at the start of the period.
- \(n\): The duration of the investment in years.

Step 3: Calculation Process:
Given information:
- Beginning Value = Rupees 10,000
- Ending Value = Rupees 14,000 (as of 2023)
- Number of years (\(n\)) = 6 years

Substituting these values into the CAGR formula:
\[ \text{CAGR} = \left( \frac{14,000}{10,000} \right)^{1/6} - 1 \]
\[ \text{CAGR} = (1.4)^{1/6} - 1 \]
Using the provided value for \((1.4)^{1/6} \approx 1.058\):
\[ \text{CAGR} \approx 1.058 - 1 = 0.058 \]
Converting to a percentage:
\[ \text{CAGR} = 0.058 \times 100% = 5.8% \]

Step 4: Conclusion:
The compound annual growth rate (CAGR) for the investment is 5.8%.