Kane is a senior portfolio analyst at AK capital. Having earned so much money at the company, he is thinking about early retirement. Kane is currently 29 years old, and he plans to retire at the age of 48 . The life expectancy of an Australian male is about 82 years. However, Kane believes that he should be able to live until the end of his 84 th year, given his above-average health. He estimates that he will need a yearly amount of $350,000 from age 49 to age 84 to live comfortably (i.e., he will need the first payment when he turns 49 and he will need his last payment when he turns 84 ). The interest rate is 6% p.a. (compounded annually) during this period. Kane's annual income is $250,000 after-tax, of which 20% would be spent on living expenses. The remaining amount would be placed in an investment fund which earns 7% p.a. (compounded annually). The first deposit will be made when he turns 30 and this will continue until he turns 48 years old (i.e., the last deposit will be made when he turns 48). He is committed to making annual deposits. Assumptions: - His income and the ratio of living expenses to annual income remain constant. - The current balance of his investment account is 0 . - No withdrawals will be made until he retires. - He will withdraw all the money by his 84 th year. Part b [4 marks] Based on the information in the second paragraph, how much in total will Kane have in his investment account when he retires at the age of 48 ? Kane is a senior portfolio analyst at AK capital. Having earned so much money at the company, he is thinking about early retirement. Kane is currently 29 years old, and he plans to retire at the age of 48 . The life expectancy of an Australian male is about 82 years. However, Kane believes that he should be able to live until the end of his 84 th year, given his above-average health. He estimates that he will need a yearly amount of $350,000 from age 49 to age 84 to live comfortably (i.e., he will need the first payment when he turns 49 and he will need his last payment when he turns 84 ). The interest rate is 6% p.a. (compounded annually) during this period. Kane's annual income is $250,000 after-tax, of which 20% would be spent on living expenses. The remaining amount would be placed in an investment fund which earns 7% p.a. (compounded annually). The first deposit will be made when he turns 30 and this will continue until he turns 48 years old (i.e., the last deposit will be made when he turns 48). He is committed to making annual deposits. Assumptions: - His income and the ratio of living expenses to annual income remain constant. - The current balance of his investment account is 0 . - No withdrawals will be made until he retires. - He will withdraw all the money by his 84 th year. Part b [4 marks] Based on the information in the second paragraph, how much in total will Kane have in his investment account when he retires at the age of 48
