A sum of Rs.20000 is invested for 15 months at the interest of 10% per annum compounded half yearly. What is the percentage gain, correct to one decimal place, at the end of the 15 months?

Half-yearly compounding at 10% p.a. means 5% per half-year. For 15 months = 5 half-years (30 months) - no, 15 months has only 2.5 half-years. Actually 15 months = 1.25 years, with half-yearly compounding we have 3 half-years (18 months) would be 3 periods, but 15 months is exactly 2.5 half-years, which means 2 full half-years plus 3 months at simple interest. Let me recalculate: P = 20000, rate = 5% per half-year. After 2 half-years: 20000 × 1.05 × 1.05 = 22050. For remaining 3 months at 10% p.a. simple interest on 22050: 22050 × (10/100) × (3/12) = 551.25. Total = 22050 + 551.25 = 22601.25. Gain = 2601.25, gain% = 2601.25/20000 × 100 = 13.0%. Option C is correct.