Harmonic mean

A SIP invests ₹6,000 at each of six monthly NAVs: 50, 40, 32, 40, 50, 62.5. (a) Compute units bought, the average cost per unit, the arithmetic mean NAV, and the approximation (6B.15). (b) Prove $H \le A$ for two prices directly, without Cauchy–Schwarz. (c) Compute the value of the holding at the last NAV and the absolute gain. Explain why the gain is large although the NAV only rose from 50 to 62.5.