(2) Retirement investment: Suppose an initial deposit of D dollars into a savings account yields a fixed percentage per year. We would like to know how much capital D a person needs to initially deposit when s/he retires to live for N years assuming an annual withdrawal of W dollars. (i) How much money needs to be initially deposited to last exactly N years when withdrawing W dollars per year (starting after the first year) out of the account? [Note: the partial sum of a geometric series is given by: P N i=1 bri−1 = b(1 − r N )/(1 − r)]. (ii) In a realistic scenario, the average person retires at 65 and the life expectancy is about 80 years. Assume a 5% yield a year and that the person needs 30, 000 per year to sustain themselves. How much does this person need to invest at retirement? (iii) Compare this to the total amount needed to live for 15 years at 30, 000 per year (= 15 × 30, 000 = 450, 000).