Direct and regular SIPs

A SIP of ₹15,000 a month runs for 25 years (300 instalments, invested at the start of each month). The portfolio earns 11% a year gross. The direct plan charges 0.65% and the regular plan 1.35% (illustrative). (a) Compute both corpora and the rupee gap. (b) Express the gap as a percentage of the direct corpus and compare it with the one-month loss $1 - \gamma$ and the 25-year lump-sum loss $1 - \gamma^{300}$ of Proposition 6B.3.2. (c) Prove that for any $n$ the SIP's proportional loss is strictly smaller than that of a lump sum held for $n$ months. (d) The distributor of the regular plan argues that the investor "only pays 0.70% a year". Write one paragraph that states the cost correctly.