W 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 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, W 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 to make annual payments starting today. He intends to make 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 W to go into overdraft if he needs to. The overdraft rate will also be 6% p.a. compounded monthly.

a. How much must W 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?