can you help me with these set of question
Nick has just turned 25 and considers joining the pension plan offered by his employer. If he joins the pension plan, Nick will need to pay annual contributions during his employment. The first contribution should be paid on his 26th birthday (i.e., in a year's time). Nick plans to retire on his 65" birthday (i.e., in 40 years' time), when he would have to pay his last contribution to the pension plan. His life expectancy is 85 years. During his retirement (i.e., until his 85th birthday), Nick wants to receive 30,000 per year, starting from his 66" birthday. The interest rate that applies to the entire period is 5% per year. a) Find the present value (today) of the cash flows that Nick wants to receive from his 66th birthday until his 85th birthday. (10 marks) b) Find the amount that Nick has to contribute to the pension plan every year during his employment to finance the cash flows he wants to receive during his retirement. (10 marks) c) Nick finds the annual contribution he has to make very high and seeks financial advice. An advisor suggests to him to retire at the age of 70 instead of 65. If he follows this advice, find the annual contribution that Nick will have to make during his employment to finance the cash flows of 30,000 per year that he wants to receive during his retirement (i.e., from his 71st birthday until his 85th birthday). Explain why this is lower than the annual contribution calculated in b). (10 marks) (IUC d) Nick is also aware of the possibility that his life expectancy may increase to 90 years, and he is concerned that he will not receive any cash flow after the age of 85. If he decides to retire at the age of 70, how much will he need to contribute to the pension plan per year during his employment to receive 30,000 per year during his retirement until the age of 90? (5 marks) Nick has just turned 25 and considers joining the pension plan offered by his employer. If he joins the pension plan, Nick will need to pay annual contributions during his employment. The first contribution should be paid on his 26th birthday (i.e., in a year's time). Nick plans to retire on his 65" birthday (i.e., in 40 years' time), when he would have to pay his last contribution to the pension plan. His life expectancy is 85 years. During his retirement (i.e., until his 85th birthday), Nick wants to receive 30,000 per year, starting from his 66" birthday. The interest rate that applies to the entire period is 5% per year. a) Find the present value (today) of the cash flows that Nick wants to receive from his 66th birthday until his 85th birthday. (10 marks) b) Find the amount that Nick has to contribute to the pension plan every year during his employment to finance the cash flows he wants to receive during his retirement. (10 marks) c) Nick finds the annual contribution he has to make very high and seeks financial advice. An advisor suggests to him to retire at the age of 70 instead of 65. If he follows this advice, find the annual contribution that Nick will have to make during his employment to finance the cash flows of 30,000 per year that he wants to receive during his retirement (i.e., from his 71st birthday until his 85th birthday). Explain why this is lower than the annual contribution calculated in b). (10 marks) (IUC d) Nick is also aware of the possibility that his life expectancy may increase to 90 years, and he is concerned that he will not receive any cash flow after the age of 85. If he decides to retire at the age of 70, how much will he need to contribute to the pension plan per year during his employment to receive 30,000 per year during his retirement until the age of 90
