Retirement Investment: Suppose an initial deposit of D dollars into a savings account yielding p% per year. We would like to know how much capital a person needs to initially depoist when he/she retires to lie for N years. (i) How much money needs to be initialy 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] (ii) In a realistic scenario, the average person retires at 65 and the life expectancy is about 80 years. Assum p=5% a year and that the person needs 30,000 per year to sustain themsselves. How much foes 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 x 30,000 =450,000).