SOA Exam ALTAM Sample Question 41

Study guide: Exam ALTAM

A corporation offers its employees a Final Salary Defined Benefit pension with an accrual rate of 2% per year of service. The Final Pensionable Salary is the salary earned in the final year of employment. The pension is paid as a single life monthly annuity-due with a 10-year guarantee.

Employees contribute 6% of pay at the end of each month throughout their period of employment.

An employee of the corporation is about to retire at age 65. The employee was hired at age 30 and has worked continuously since then. Their starting salary was 40,000 per year.

You are given the following additional information:

(i) Salaries increase monthly at a rate of 3.6% per year compounded monthly.

(ii) The two term Woolhouse Formula is used for valuing the retirement pension.

(iii) Mortality is assumed to follow the Standard Ultimate Life Table.

(iv) The valuation interest rate is 5%.

(v) Members have the option of taking a lump sum at retirement equal to the expected present value of their retirement pension, using the valuation assumptions.

Part a (2 points)

Show that the employee's monthly pension is 8050 to the nearest 10. You should calculate the value to the nearest 0.1.

Part b (2 points)

Calculate the expected present value of the employee's retirement pension at age 65.

Part c (2 points)

Show that the accumulated value of the employee's contributions at retirement, assuming interest of 9.6% per year compounded monthly, is 995,500 to the nearest 100. You should calculate the value to the nearest 10.

Part d (1 point)

Assume that the employee takes the lump sum option. State with reasons whether the internal rate of return (IRR) that the employee has earned on their contributions is more than or less than 9.6% per year compounded monthly.

Part e (1 point)

Employees have the option to take a higher monthly pension at retirement without a guarantee period. The revised benefit has the same expected present value at age 65 as the standard benefit.

Calculate the revised monthly payment.

Part f (2 points)

(i) Define adverse selection.

(ii) Explain how adverse selection might impact the pension plan's costs based on the employees' selection of annuity with guarantee, annuity without guarantee, and lump sum.

(This is Question 6 from the Fall 2018 Written Answer exam.)

Answer this question and see the worked solution