If an investment of Rs. 12000 becomes Rs. 72000 in 4 years, then the compound annual growth rate is:

$(\sqrt[4]{6}-1)×100\%$

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

Given:

Initial value = 12000

Final value = 72000

Time = 4 years

CAGR formula:

$\text{CAGR} = \left(\frac{\text{Final}}{\text{Initial}}\right)^{\frac{1}{t}} - 1$

$= \left(\frac{72000}{12000}\right)^{\frac{1}{4}} - 1$

$= (6)^{\frac{1}{4}} - 1$

$= \sqrt{\sqrt{6}} - 1$

Numerical value:

$6^{0.25} \approx 1.565$

CAGR ≈ $1.565 - 1 = 0.565$

CAGR ≈ 56.5% per annum