A sum doubles in 4 years at a certain rate of compound interest. In how many years does it amount to 8 times itself at the same rate?

A sum doubles in 4 years at a certain rate of compound interest.

$$2P=P\left(1+\frac{R}{100}\right)^4$$

$$2 = (1+\frac{R}{100})^4$$    Eq.(i)

Let's assume that amount became 8 times in 't' years.

$$8P=P\left(1+\frac{R}{100}\right)^t$$

$$8 = (1+\frac{R}{100})^t$$    Eq.(ii)

Apply cube in Eq.(i).

$$2^3=(1+\frac{R}{100})^{4\times\ 3}$$

$$8=(1+\frac{R}{100})^{12}$$    Eq.(iii)

Now compare Eq.(ii) and Eq.(iii).

So t = 12 years