A sum of Rs 4000 becomes Rs 5800 in 3 years, when invested in a scheme of simple interest. If the same sum is invested in a scheme of compound interest with same yearly interest rate (compounding of interest is done yearly), then what will be the amount (in Rs) after 2 years?

Principal sum = Rs. 4000 and time period = 3 years

=> Amount after simple interest = Rs. 5800

Thus, simple interest = Rs. (5800-4000) = Rs. 1800

Let rate of interest = $$r\%$$

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

=> $$\frac{4000\times r\times3}{100}=1800$$

=> $$120r=1800$$

=> $$r=\frac{1800}{120}=15\%$$

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

= $$4000(1+\frac{15}{100})^2$$

= $$4000(1+\frac{3}{20})^2=4000(\frac{23}{20})^2$$

= $$4000\times\frac{529}{400}$$

= $$10\times529=Rs.$$ $$5290$$

=> Ans - (C)