A sum of money is lent for 2 years at 10% per annum on compound interest. It yields Rs 8.81 more when compounded semi-annually than compounded annually. What is the sum lent?

For annual compounding at 10% for 2 years: A = P(1.1)² = 1.21P. For semi-annual: rate = 5% per period, periods = 4, so A = P(1.05)⁴ = P × 1.2155. Difference = 0.0055P = Rs 8.81. Therefore P = 8.81 ÷ 0.0055 = Rs 1600. The key is understanding that semi-annual compounding gives slightly higher returns due to more frequent compounding periods.