You are 65 years old and are considering the purchase of a pension annuity that would provide annual income of 100000/a_65 starting immediately. Your alternative is to invest the $100,000 in a mutual fund earning a random return g (where E[g] = 9% annually and SD = 20%) and to withdraw c each year; this is called self annuitization. Assume that the force of mortality is constant at X = 3.67%. What is the probability you will run out of money while you are still alive?