A sum of Rs. 16000 deposited at compound interest becomes double after 5 years. How much will it be after 20 years?

Rs.256000

Amount = P (1+ \(\frac{r}{100}\))^t

ATQ,

⇒ 2P = P (1+ \(\frac{r}{100}\))⁵      

⇒ 2 = (1+ \(\frac{r}{100}\))⁵               

⇒ (2)⁴ = (1+ \(\frac{r}{100}\))²⁰

⇒ 16 = (1+ \(\frac{r}{100}\))²⁰

⇒ So, in 20 years it becomes 16 times. Therefore,

⇒ Amount = 16P → 16 × 16000 = 256000/-

OR

ATQ,

P   →    5yr   →     2P

              ↓              ↓

             ×4        power 4*

              ↓              ↓

P   →    20yr   →    (2)⁴P

                      →   16P

⇒ So, in 20 years it becomes 16 times. Therefore,

⇒ Amount = 16P → 16 × 16000 = 256000/-