The value of a SIP customer

A customer starts a SIP of ₹5,000 a month for 15 years. Holdings grow at 10% a year net of fees; 8% of customers leave each year; the AMC discounts at 12% a year; convert all rates to monthly. (a) Compute the present value of the AMC's fees at a fee yield of 0.60% (Proposition 6B.5.2). (b) Compute the present value of a distributor's trail of 0.75% on the same customer. (c) Recompute (a) with annual attrition of 15%. What does the comparison say about where an AMC should spend money? (d) Why does (6B.13) need $q < 1$? Give the economic interpretation of a customer with $q \ge 1$.