Question 1 (Group Project, 20 marks) Paul is celebrating his 43"d birthday today and is his family. planning for a retirement savings programe 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 expected to increase with the inflation rate of 3% per year. It takes his daughter 4 years t 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 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 70 birthday through the 80th birthday. He plans to leave $10,000,000 to his family at his 90h 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 guarterly 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 60h 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 (3 marks) fund to the high-yield account)? (b) What is the present value (at Paul's 43"d birthday) of the total costs for sending her daughter to (5 marks) the university for undergraduate study? (c) How much must Paul deposit every quarter in order to meet all his withdrawal needs? (12 marks) Question 1 (Group Project, 20 marks) Paul is celebrating his 43"d birthday today and is his family. planning for a retirement savings programe 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 expected to increase with the inflation rate of 3% per year. It takes his daughter 4 years t 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 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 70 birthday through the 80th birthday. He plans to leave $10,000,000 to his family at his 90h 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 guarterly 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 60h 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 (3 marks) fund to the high-yield account)? (b) What is the present value (at Paul's 43"d birthday) of the total costs for sending her daughter to (5 marks) the university for undergraduate study? (c) How much must Paul deposit every quarter in order to meet all his withdrawal needs? (12 marks)
