The annual sales of a company in the year 2000 was Rs. 1000 and in the year 2005 was Rs. 2490. Find the compounded annual growth rate of sales in the given period of the same company.

Options

A. a. `14.289%`
B. b. `10%`
C. b. `20%`
D. d. `11%`

Answer

To find the compounded annual growth rate (CAGR) of sales for the company from the year 2000 to 2005, we can use the following formula:

\[ CAGR = \left( \frac{V_f}{V_i} \right)^{\frac{1}{n}} - 1 \]

Where:
- \( V_f \) = final value (sales in 2005)
- \( V_i \) = initial value (sales in 2000)
- \( n \) = number of years

### Step-by-Step Solution:

1. **Identify the values:**
- \( V_i = 1000 \) (sales in 2000)
- \( V_f = 2490 \) (sales in 2005)
- \( n = 2005 - 2000 = 5 \) years

2. **Substitute the values into the CAGR formula:**
\[ CAGR = \left( \frac{2490}{1000} \right)^{\frac{1}{5}} - 1 \]

3. **Calculate the fraction:**
\[ \frac{2490}{1000} = 2.49 \]

4. **Now substitute this back into the formula:**
\[ CAGR = (2.49)^{\frac{1}{5}} - 1 \]

5. **Calculate \( (2.49)^{\frac{1}{5}} \):**
- You can use a calculator or logarithms to find this value.
- \( (2.49)^{\frac{1}{5}} \approx 1.215 \)

6. **Subtract 1 from the result:**
\[ CAGR \approx 1.215 - 1 = 0.215 \]

7. **Convert to percentage:**
\[ CAGR \approx 0.215 \times 100 = 21.5\% \]

### Final Answer:
The compounded annual growth rate (CAGR) of sales from 2000 to 2005 is approximately **21.5%**.

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