If an investment of Rs. 12000 becomes Rs. 72000 in 4 years, then the…

The correct answer is Option (4) → \((\sqrt[4]{6}-1)\times 100\%\)

For a beginning value \(V_0\) and an ending value \(V_n\) after n years, the compound annual growth rate is

    \( \displaystyle \text{CAGR} = \left[\left(\frac{V_n}{V_0}\right)^{1/n} - 1\right] \times 100\% \)

Here \(V_0 = 12000\), \(V_n = 72000\) and n = 4:

    \( \displaystyle \frac{V_n}{V_0} = \frac{72000}{12000} = 6 \)

    \( \text{CAGR} = \left(6^{1/4} - 1\right) \times 100\% = (\sqrt[4]{6} - 1) \times 100\% \)

Numerically, \(\sqrt[4]{6} \approx 1.565\), so the CAGR is about 56.5% per year.

CBSE Applied Mathematics (Class XII):
Compound Annual Growth Rate