10. Roshan invests ₹ \( 2,40,000 \) for 2 years at \( 10 \% \) per annum compounded anually. If the income tax at \( 20 \% \) is deducted at the end of each year on the interest accrued, find the amount he will receive at the end of 2 years.

We start with an investment of ₹2,40,000 at a nominal rate of 10% per annum, compounded annually. However, at the end of each year the interest earned is subjected to a 20% income tax. Step 1: Calculate the Interest for Year 1 • Interest before tax = 10% of ₹2,40,000 = ₹24,000 • Tax on interest = 20% of ₹24,000 = ₹4,800 • Net interest earned = ₹24,000 − ₹4,800 = ₹19,200 At the end of Year 1, the amount becomes: Principal after Year 1 = Original principal + Net interest = ₹2,40,000 + ₹19,200 = ₹2,59,200 Step 2: Calculate the Interest for Year 2 Now, the new principal is ₹2,59,200. Compute the second year’s interest based on this amount. • Interest before tax = 10% of ₹2,59,200 = ₹25,920 • Tax on interest = 20% of ₹25,920 = ₹5,184 • Net interest earned = ₹25,920 − ₹5,184 = ₹20,736 At the end of Year 2, the final amount becomes: Final amount = Principal after Year 1 + Net interest for Year 2 = ₹2,59,200 + ₹20,736 = ₹2,79,936 Thus, at the end of 2 years, Roshan will receive ₹2,79,936.