You would like to start planning your retirement. You are now 35 years old and plan to retire at the age of 67. You plan to withdraw a considerable sum at the end of each month, starting exactly one month past your 67th birthday, until the age 89 The effective annual rate is 6%: a. Suppose that you would want a monthly withdrawal amount of $10,000 once you retire. If you would like to deposit on a quarterly basis (meaning at the end of each quarter), how much do you need to deposit at the end of each quarter until the age of 67, included? Your parents, happy by your decision, promised to deposit you, once you retire, an additional $100,000 to your retirement account. What is the amount that you would be able to decrease from your quarterly deposits if you would like to stay with your original withdrawal plan? Suppose that instead of what was written in section b, on your 67th birthday, the retirement plans manager offered you a new

withdrawal plan. According to the new plan, you will get monthly allowance forever. For this you will have to pay 10% on any withdrawal from the deposit account. What would be your monthly withdrawal, until eternity, according to the new plan? Compared to item A of this question, if the deposits are made at the beginning of each quarter and the withdraws at the beginning of each month, would your answer to item a change? Explain without calculating the new monthly payment