Z wants to plan for the future by investing on a regular basis. The investment plan needs to provide for his retirement and the university education of his small child. His childs university education will require a series of 4 annual withdrawals starting in exactly 16 years. Each withdrawal would have the same purchasing power as $15000 today. Inflation is expected to be 2.5% p.a. indefinitely. When he retires, Z will make annual withdrawals starting in exactly 41 years. Each withdrawal will be $50000. He plans to make a total of 20 withdrawals. He intends making annual payments starting today. He intends making his last deposit in exactly 40 years. Interest rates are, and are expected to remain at 6% p.a. compounded monthly. The bank manager will permit Z to go into overdraft if he needs to. The overdraft rate will also be 6% p.a. compounded monthly. a. How much must Z deposit annually to achieve his plan? b. What will his bank balance be immediately after he has made the 4th withdrawal for his childs education?