If a certain sum becomes 4 times in 4 years at compound interest, then in how many years, it will become 64 times?

Let principal sum = Rs. $$P$$ and rate of interest = $$r\%$$

Amount under compound interest = $$P(1+\frac{r}{100})^T$$

Thus, after 4 years

=> $$P(1+\frac{r}{100})^4=4P$$

=> $$(1+\frac{r}{100})^4=4$$

=> $$(1+\frac{r}{100})=(4)^{\frac{1}{4}}$$ -------------(i)

Now, Let after $$t$$ years sum becomes 64 times

=> $$P(1+\frac{r}{100})^t=64P$$

=> $$(4)^{\frac{t}{4}}=(4)^3$$

Comparing the exponents, we get :

=> $$\frac{t}{4}=3$$

=> $$t=4\times3=12$$ years

=> Ans - (B)