You are an actuary for a pension plan that promises to pay a monthly retirement benefit of $2,500 starting at age 65 to its employees who have completed 30 years of service. The plan currently has 1,000 active employees, each with an expected remaining service life of 15 years. The plan's assets are invested in a fixed-income fund with an expected annual interest rate of 5%. The pension plan uses the following assumptions in its valuation:

• The probability of an employee dying in any given year follows a uniform distribution between ages 50 and 85.
• The probability of an employee retiring in any given year follows a uniform distribution between ages 55 and 65.
• The expected annual salary increase for the employees is 2%.

Calculate the actuarial present value (APV) of the pension plan's liabilities.

(20 marks)