A sum of money invested at compound interest doubles itself in 6 year…

ATQ,

P = 1   →    6yr       →        2 (Amount)

                    ↓                    ↓

                  ×3              power 3*

                    ↓                    ↓

P = 1   →    18yr      →     (2)³ = 8 times

⇒ So, in 18 years it becomes 8 times

 

OR

Amount = P (1+ \(\frac{r}{100}\))^t

ATQ,

⇒ 2P = P (1+ \(\frac{r}{100}\))⁶   

⇒ 2 = (1+ \(\frac{r}{100}\))⁶

⇒ (2)³ = (1+ \(\frac{r}{100}\))¹⁸

⇒ 8 = (1+ \(\frac{r}{100}\))¹⁸

⇒ So, in 18 years it becomes 8 times.