Question 3 (20 marks)

Mr. Yiu just wins a lottery of $6,261,362 today. He opens a bank account and puts the whole amount in the bank account which gives him 3.4% p.a. interest rate.

He will withdraw $100,000 from the account today. From next year onwards he will withdraw an amount that is 10% more than the previous years amount. That means he will withdraw $100,000 x (1+10%) next year, and $100,000 x (1+10%)² two years later and $100,000 x (1+10%)³ three years later, and so on. (Hint: This is similar to the education fund question.)

1. Based on Mr. Yius withdrawal plan above, calculate the number of years he can withdraw money from the account. (12 marks)

2. Suppose Mr. Yiu would like to be able to withdraw money for 30 years. Calculate the rate of return (nominal rate) he needs for his money.(8 marks)