The difference between compound interest and simple interest on a sum for 2 year at 20% per annum is Rs 200. If the interest is compounded half yearly, then what is the difference (in Rs) between compound and simple interest for 1st year?

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

Rate of interest = 20% and time period = 2 years

Compound interest = $$P [(1 + \frac{R}{100})^T - 1]$$

= $$100x [(1 + \frac{20}{100})^2 - 1]$$

= $$100x [(\frac{6}{5})^2 - 1] = 100x (\frac{36 - 25}{25})$$

= $$100x \times \frac{11}{25} = 44x$$

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

= $$\frac{100x \times 20 \times 2}{100} = 40x$$

=> Difference between simple and compound interests = $$44x - 40x = 200$$

=> $$x = \frac{200}{4} = 50$$ ---------------(i)

If interest is compounded half yearly, => Compound interest for 1st year = $$P[(1+\frac{R}{200})^{2T}-1]$$

= $$100x[(1+\frac{20}{200})^2-1]=100x[(\frac{11}{10})^2-1]$$

= $$100x (\frac{121-100}{100})=21x$$

Similarly, Simple interest for 1st year = $$\frac{100x\times 20\times1}{100}=20x$$

$$\therefore$$ Required difference = $$21x-20x=x=Rs.$$ $$50$$

=> Ans - (A)