6. Today is your 22nd birthday and you are evaluating different personal finance and retirement plans. You are considering 3 options to save for retirement: a. Starting when you're 22, invest $100 per month for 43 years. b. Starting when you're 40 , invest $500 per month for 25 years. c. Gamble that your rich uncle will die when you are about 60 and you will inherit his money. In option a and option b, for simplicity, assume you start saving one month after your 22add birthday and one month after 40 birthday respectively and in both cases the last deposit made on your 65th birthday. In all 3 options, you expect to be able to earn 0.7% monthly rate. a) How much will options (a) and (b) provide for retirement at age 65 ? b) How much money will your rich uncle have to leave you at age 60 in order for you to retire at age 65 with as much money as in option (a)? c) Suppose you choose option (c). On your 60 th birthday party your uncle shows up healthier than ever. Now you have to seriously plan for your retirement on your own for the remaining 5 years. How much do you have to invest every month so you can retire at 65 with the same amount of money as if you have chosen option (a)? d) Suppose you choose option (a), after retirement at age 65, you plan to make monthly withdrawal from the fund for 20 years. How much you can withdraw each month if you the account balance will be depleted when you are 85 ? How much you can withdraw each month if you want to the account still has a balance of $10,000 when you are 85