A sum of money on compound interest becomes double of itself in 3 years. How many years will it take for the amount to become eight times of itself at the same rate of interest.?

Correct option is B

Given:

Amount becomes double

Time =3 years

Formula Used:

Compounded Amount =$$Principle \times (1+ \frac{r}{100})^{t}$$​​

Amount = Principle + Interest

Solution:

Let Principle be P

Amount = 2$$\times$$​  Principle

​$$2P = P (1+ \frac{r}{100})^{3}$$​​

​$$2 = (1+ \frac{r}{100})^{3}$$​   ….(1)

$$8P = P (1+ \frac{r}{100})^{t}$$​

​$$2^{3} = (1+ \frac{r}{100})^{t}$$​​

​$$[ (1+ \frac{r}{100})^{3}]^{3} =(1+ \frac{r}{100})^{t}$$​  (From eq(1))

​$$(1+ \frac{r}{100})^{9}=(1+ \frac{r}{100})^{t}$$​​

t = 9 years