An annuity provides insurance against out-living one's financial resources. LEICO, a life insurance company, takes a deposit from customers at age 60 years, and returns an annual payment of Rs. 5000 till their death. (a) Calculate the break-even deposit for LEICO if average population-wide life expectancy is 80 years. Assume a 5% interest rate. (b) If potential customers have a sense of their life expectancy, based on factors such as the longevity of their parents, who will purchase the annuity with the deposit you have calculated above? (c) If life expectancy is uniformly distributed in the population (up to a maximum of 100 years) and potential customers have a sense of their life expectancy, what is the deposit that LEICO will ultimately end up charging? Who will finally buy this annuity?