Suppose that your initial wealth is 1000000 and you must decide in each of the following 3 periods how much of your wealth to invest and how much to consume. Assume the utility you attain from consuming the amount x during a period is x and that the objective is to maximize the sum of the utilities you obtain in 3 periods. Assume also that an investment earns a fixed rate of return 5% per period. Let Vn(x) denote the maximal sum of utilities that can be attained when your current fortune is x and n additional periods remain. Derive an iterative relation for Vn(x) and determine the amounts to consume and to invest in each of the 3 periods.