A sum of money becomes eigth times in 3 years if the rate is compounded annually. In how much time, the same amount at the same compound interest rate will become sixteen times?

A 6 years

B 4 years

C 8 years

D 5 years

E None of these

Correct Answer: Option B

Let P is the principal amount.

Then, amount received at the end of three years = 8P

According to the given condition,

\(\Rightarrow 8P = P{\left( {1 + \frac{r}{{100}}} \right)^3}\;\)

⇒ 2 = 1 + r/100

⇒ R = 100 %

Now, to get amount as 16 times of the principal,

\(\Rightarrow 16P = P{\left( {1 + \frac{{100}}{{100}}} \right)^t}\)

⇒ T = 4 years.