A sum becomes 6 times of itself in 4 years at compound interest (interest is compounded annually). In how many years will the sum becomes 216 times of itself?

Let Principal be Rs.P
Let Rate of interest be R%
Time Period = 4 years
Amount after 4 years = Rs.6P
$$P(1+\dfrac{R}{100})^4 = 6P$$

=> $$(1+\dfrac{R}{100})^4 = 6$$

=> $$(1+\dfrac{R}{100}) = 6^\frac{1}{4}$$ -- (1)
Let the amount after T years be Rs.216P

$$P(1+\dfrac{R}{100})^T = 216P$$

=> $$(1+\dfrac{R}{100})^T = 216$$

Substituting (1) in above equation
=> $$(6^\frac{1}{4})^T = 6^3$$
=> $$6^\frac{T}{4} = 6^3$$
=> $$\dfrac{T}{4} = 3$$

=> $$T = 12$$
Therefore, In 12 years, the given sum becomes 216 times of itself.