A pension scheme provides a benefit on death in service of 4 times the member’s salary at the date of death. Normal Pension Age is 65. State a formula, without using commutation functions, for the present value of this benefit to a life aged 35 exact with salary of £25,000 who has just received a salary increase. Define all symbols used. Sol - In the numerator 1st term should be \( S_{x+t}\) instead \(S_{x+t+1}\) and denominator 1st term should be \( S_{34}\) or (\( S_{35}\) if considering salary increased just now) instead \(S_{36}\) Which is correct and why?
It's because of the way that sx has been defined. Normally (in the course notes and in the Tables) sx relates to the salary in the year beginning at age x. This would give your answer (s35+t in the numerator sum and s35 in the denominator). But they have defined sx to be the salary in the year ENDING at exact age x - hence every s-subscript needs to have +1 added to the age. For pension formulae there are no standard definitions. In your answer you must ALWAYS define all you symbols. I would do the same as you - use our normal definition for sx - but you would HAVE to state the definition in your answer to earn full marks. The definitions are very important for "deriving formulae" type questions. Robert
