The difference between the simple interest and compound interest(interest is compounded half yearly) on a sum at the rate of 25% per annum for one year is ₹ 4375. What will be the principal?

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

Rate of interest = $$r=25\%$$ and time = $$t=1$$ year

Simple interest = $$\frac{P\times r\times t}{100}$$

= $$\frac{100x\times25\times1}{100}=Rs.$$ $$25x$$

Compound interest (compounded half yearly for 1 year) = $$P[(1+\frac{r}{200})^2-1]$$

= $$100x[(1+\frac{25}{200})^2-1]$$

= $$100x[(\frac{9}{8})^2-1]$$

= $$100x\times(\frac{17}{64})=Rs.$$ $$26.5625x$$

$$\therefore$$ Difference = $$26.5625x-25x=4375$$

=> $$x=\frac{4375}{1.5625}=2800$$

$$\therefore$$ Principal sum = $$100\times2800=Rs.$$ $$2,80,000$$

=> Ans - (A)