Suppose a company has a defined benefit pension plan for its employees. The plan promises to pay a monthly benefit of $1,500 to each retiree for 20 years, starting at age 65. The plan assumes a probability of survival of 95% for each retiree during the payment period. The company has 1,000 employees who are currently 45 years old, and the plan assumes an interest rate of 4% and an annual salary increase of 2%.

a) What is the expected future liability of the plan for the company? b) What is the present value of the expected future liability using a discount rate of 4%? c) If the company wants to fully fund the plan in 20 years, what should be the monthly contribution per employee to the pension plan?

Show all calculations and explain the steps.

(20 marks)