There is 40% increase in an amount in 8 years at simple interest. What will be the compound interest (in rupees) of Rs 30000 after 2 years at the same rate?

Let the principal = $$Rs. 100x$$

=> Amount after simple interest = $$\frac{140}{100} \times 100 = Rs. 140x$$

=> Simple interest = $$140x - 100x = Rs. 40x$$

Simple interest = $$\frac{P \times R \times T}{100}$$

=> $$40x = \frac{100x \times 8 \times R}{100}$$

=> $$R = \frac{40}{8} = 5\%$$

Compound interest of Rs. 30,000 for 2 years = $$P [(1 + \frac{R}{100})^T - 1]$$

= $$30,000 [(1 + \frac{5}{100})^2 - 1]$$

= $$30,000 [(\frac{21}{20})^2 - 1]$$

= $$30,000 \times \frac{441 - 400}{400} = 30,000 \times \frac{41}{400}$$

= $$75 \times 41 = Rs. 3,075$$

=> Ans - (D)