Fee drag on a lump sum

₹25 lakh is invested for 15 years. The underlying portfolio earns 11% a year gross. An index fund charges 0.20%; an active fund's regular plan charges 1.70% (illustrative). (a) Compute both terminal values and their ratio, assuming the active fund earns the index return before fees. (b) Compute the bounds (6B.8) and the continuous approximation $e^{-\Delta c\,T}$. Which is closer, and why? (c) What annual gross alpha must the active fund earn, every year, to match the index fund's terminal wealth?