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?

How were these answers obtained?

16 years Education Start Annual purchasing power Expected inflation rate # withdrawals $ 15,000.00 2.50% 4 Retirement Annual withdrawal Starting in # withdrawals $ 50,000.00 41 years 20 Deposits Start today Last deposit in Annual deposits 40 years 6.00% p.a. Rate Compounds/yr 12 a. PV of deposits must equal PV of all withdrawals. There are two sets of withdrawals, the deferred growth annuity and the deferred annuity. EAR 6.168% Deferred growth annuity PV $ 22,267.58 $ 32,454.98 Deferred annuity PV $ 51,632.96 Total PV $ 84,087.94 PV t=-1 79202.88 Annual deposit $ 5,344.47 b. Amount in bank immediately after 4ht withdrawal at t=19 will equal the FV of the 20 deposits less the FV of the deferred growth annuity of withdrawals. Future value of deposits Future value of withdrawals $ 200,182.59 $ 101,191.37 Bank account $ 98,991.22 16 years Education Start Annual purchasing power Expected inflation rate # withdrawals $ 15,000.00 2.50% 4 Retirement Annual withdrawal Starting in # withdrawals $ 50,000.00 41 years 20 Deposits Start today Last deposit in Annual deposits 40 years 6.00% p.a. Rate Compounds/yr 12 a. PV of deposits must equal PV of all withdrawals. There are two sets of withdrawals, the deferred growth annuity and the deferred annuity. EAR 6.168% Deferred growth annuity PV $ 22,267.58 $ 32,454.98 Deferred annuity PV $ 51,632.96 Total PV $ 84,087.94 PV t=-1 79202.88 Annual deposit $ 5,344.47 b. Amount in bank immediately after 4ht withdrawal at t=19 will equal the FV of the 20 deposits less the FV of the deferred growth annuity of withdrawals. Future value of deposits Future value of withdrawals $ 200,182.59 $ 101,191.37 Bank account $ 98,991.22