The Simple interest accrued on a certain principal is Rs.1600 in 4 years at the rate of 8 percent per annum. What would be the compound interest accrued on twice of that principal at the rate of 10 percent per annum in 2 years?

Correct option is A

​$$\text{Given: SI} = 1600,\quad R = 8\%,\quad T = 4 \text{ years}$$

$$Rightarrow 1600 = \frac{P \cdot 8 \cdot 4}{100}$$

$$\Rightarrow 1600 = \frac{32P}{100}$$

$$\Rightarrow P = \frac{1600 \cdot 100}{32} = 5000$$

$$\text{Now, for CI: Principal} = 2 \cdot 5000 = 10000,\quad R = 10\%,\quad T = 2$$

$$CI = P\left(1 + \frac{R}{100}\right)^T - P$$

$$= 10000\left(1 + \frac{10}{100}\right)^2 - 10000$$

$$= 10000 (1.1)^2 - 10000$$

$$= 10000 \cdot 1.21 - 10000$$

$$= 12100 - 10000= \boxed{₹2100}$$​​​