Question

Paul is celebrating his 43rd birthday today and is planning for a retirement savings programe for
his family.

[Planned expenses]

- Paul’s daughter is now 6 years old and he plans to send her to a top local university in 12 years.
Currently, the cost of studying (tuition fees and living expenses) is $150,000 per year, but it is
expected to increase with the inflation rate of 3% per year. It takes his daughter 4 years to
complete her undergraduate study, and it is assumed that he will have to pay the tutition fees
and living expenses for his daughter on his 55th, 56th, 57th and 58th birthdays.

- Besides, he would need $2,000,000 to take his wife for a round-the-world trip at their 30th
anniversary when he reaches 62.

- Paul is planning to retire at the age of 65. He estimates that he will need $30,000 a month to
enjoy his retirement years with his wife, with the first withdrawal on his 65th birthday and the
last withdrawal on his 90th birthday.

- He would also like to donate $40,000 semiannually to his university, starting from his 70th
birthday through the 80th birthday.

- He plans to leave $10,000,000 to his family at his 90th birthday.

[Planned savings and cash inflows]
- Eight years ago, Paul joined his employer’s retirement plan that paid him 6% interest
(compounded monthly). At the end of each month, he deposited $5,000 into the retirement
account. He is planning to move all the funds from his retirement account to a high-yield
savings account after he made the last deposit today.

- In addition, he plans to make a quarterly deposit to the high-yield savings account, with the
first deposit to be made a quarter from today and the last deposit one year before his retirement
(i.e. on his 64th birthday). He expects to earn a quarterly return of 3.7971% from the high-yield
account. When he retires, he will have to move all his money to a low-risk account that enables
him to withdraw money whenever he needs. It is expected that the low-risk account will pay
him an interest of 2% (compounded semiannually).

- He expects to stay in his company until he retires and receive a loyalty bonus of $80,000 at his
60th birthday. The loyalty bonus will be deposited to the high-yield account as well.

(a) How much does Paul currently have in his employer’s retirement account (before he moves his
fund to the high-yield account)?

(b) What is the present value (at Paul’s 43rd birthday) of the total costs for sending her daughter to
the university for undergraduate study?

(c) How much must Paul deposit every quarter in order to meet all his withdrawal needs?

Answer 1