A sum of money become double of itself in 4 years if compounded annually. It would amount to 32 times of itself at the same rate of interest in:

20 years

Amount = P (1+ \(\frac{r}{100}\))^t

ATQ,

⇒ 2P = P (1+ \(\frac{r}{100}\))⁴     

⇒ 2 = (1+ \(\frac{r}{100}\))⁴              

⇒ (2)⁵ = (1+ \(\frac{r}{100}\))²⁰

⇒ 32 = (1+ \(\frac{r}{100}\))²⁰

⇒ So, in 20 years it becomes 32 times.

OR

ATQ,

P = 1   →    4yr   →     2  (Amount)

                    ↓            ↓

                  ×5        power 5*

                   ↓             ↓

P = 1  →    20yr   →  (2)⁵ = 32

⇒ So, in 20 years it becomes 16 times.