A sum of Rs 2000 becomes Rs 3645 in 2 years at a certain rate of compound interest. What will be the sum (in Rs) after 4 years?

Principal amount = Rs. 2000

Amount after 2 years = Rs. 3645

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

=> $$2000(1+\frac{r}{100})^2=3645$$

=> $$(1+\frac{r}{100})^2=\frac{3645}{2000}=1.8225$$

Squaring both sides, => $$(1+\frac{r}{100})^4=3.32150625$$ ----------------(i)

$$\therefore$$ Sum after 4 years = $$P(1+\frac{r}{100})^4$$

Substituting value from equation (i), we get :

= $$2000\times3.32150625=Rs.$$ $$6643.0125$$

=> Ans - (B)