"A pension scheme provides a pension of 1/60 of career average salary in respect of each full year of service, on age retirement between the ages of 60 and 65. A proportionate amount is provided in respect of an incomplete year of service. At the valuation date of the scheme, a new member aged exactly 40 has an annual rate of salary of £40,000. Calculate the expected present value of the future service pension on age retirement in respect of this member, using the Pension Fund Tables in the Formulae and Tables for Actuarial Examinations. In the solution, there is R bar 40, but since retirement is only between 60 and 65, shouldn't the ans. be 20*M bar 40 + R bar 60?
If you are using the tables, they already have the embedded assumptions for mortality, ill health, age retirement (between 60 and 65), etc. If you look at the regular M's they are all the same, so for a final salary scheme adding p*M plus R would give the same result as using R at earlier age. Here it is a career average, so the benefit is not 20 times M bar 40 (plus R60) since the M bar 40 is on age 40 salary levels. You want each year between 40 and 60 to be based on that year's salary levels.
