A sum becomes 8 times of itself in 7 years at the rate of compound interest (interest is compounded annually). In how many years will the sum becomes 4096 times of itself?

Let Principal be Rs.P
Then, Amount after 7 years = Rs.8P
Let rate of interest = R%
$$P(1+\dfrac{R}{100})^7 = 8P$$

$$(1+\dfrac{R}{100})^7 = 8$$

$$(1+\dfrac{R}{100}) = 8^{\frac{1}{7}}$$ -- (1)

Let Amount after T years be Rs.4096P
$$P(1+\dfrac{R}{100})^T = 4096P$$

=> $$(1+\dfrac{R}{100})^T = 4096$$

Substituting (1) in above equation
=> $$(8^\frac{1}{7})^T = 8^4$$
=> $$8^\frac{T}{7} = 8^4$$
=> $$\dfrac{T}{7} = 4$$
=> $$T = 28$$
Therefore, In 28 years, the given principal will become 4096 times of itself.