A sum of money becomes 27 times of itself in 18 years at compound interest. How much times will it become in 30 years?

243 times

ATQ,

P = 1   →  18yr   →   27 or 3³  (Amount)

                    ↓                    ↓

                  ×1/3         cube-root*

                    ↓                    ↓

P = 1   →    6yr      →        (3)¹ = 3

                    ↓                    ↓

                  ×5              power 5*

                    ↓                    ↓

P = 1   →    30yr      →     (3)⁵ = 243

⇒ So, in 30 years it becomes 243 times

OR

Amount = P (1+ \(\frac{r}{100}\))^t

ATQ,

⇒ 27P = P (1+ \(\frac{r}{100}\))¹⁸    

⇒ 27 = (1+ \(\frac{r}{100}\))¹⁸             

⇒ (3)³ = (1+ \(\frac{r}{100}\))¹⁸

⇒ 3 = (1+ \(\frac{r}{100}\))⁶

⇒ (3)⁵ = (1+ \(\frac{r}{100}\))³⁰

⇒ 243 = (1+ \(\frac{r}{100}\))³⁰

⇒ So, in 30 years it becomes 243 times.