An amount doubles itself at compound interest in 5 years. How many years will it take to make the amount 16 times itself ?

Let the rate of interest be R. 

The amount doubles itself at compound interest in 5 years. 

$$P\times\left(1+\dfrac{R}{100}\right)^5=2P$$

$$1+\dfrac{R}{100}=2^{\frac{1}{5}}\rightarrow1$$

We need to find the number of years it will take to make the amount 16 times of the original. Let it be n years.

$$P\times\left(1+\dfrac{R}{100}\right)^{n}=16P$$

$$P\times\left(2^{\frac{1}{5}}\right)^n=16P$$

$$2^{\frac{n}{5}}=2^4$$

$$\dfrac{n}{5}=4$$

$$n=20$$ years.