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: Understanding the Concept:
The Compound Annual Growth Rate (CAGR) is the mean annual growth rate of an investment over a specified period longer than one year. It represents the constant rate at which the investment would have grown if it had compounded at the same rate each year.
Step 2: Key Formula or Approach:
The formula for CAGR is: \[ \text{CAGR} = \left( \frac{\text{Ending Value}}{\text{Beginning Value}} \right)^{1/n} - 1 \] where: - Ending Value is the value of the investment at the end of the period. - Beginning Value is the value of the investment at the start of the period. - \(n\) is the number of years.
Step 3: Detailed Explanation:
From the problem statement: - Beginning Value = Rupees 10,000 (the initial investment) - Ending Value = Rupees 14,000 (the value at the end of the last year, 2023) - Number of years (\(n\)) = 6 years (the investment was held for 6 years)
Now, substitute these values into the CAGR formula: \[ \text{CAGR} = \left( \frac{14,000}{10,000} \right)^{1/6} - 1 \] \[ \text{CAGR} = (1.4)^{1/6} - 1 \] The problem provides the value for \((1.4)^{1/6} \approx 1.058\). \[ \text{CAGR} \approx 1.058 - 1 = 0.058 \] 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) of the investment is 5.8%.