I have a few queries about CT5. Q&A Bank 2, Question 2.9 Why does 'supercript2 A 60:2' - D62/D40 supercsript2A60 = 0.23723 - (802.4/882.85)0.26440 not work out? Chapter 14, page 26 Members joining after age 25, restricted to 40 years of service. Why does future Mx'bar' now sum to 64 (ie NPA - x -1) rather than 65, as would appear consistent with page 25? Should it not also be (<= 65) rather than (<=64), with retirement at exact NPA defined? - ie Could they not also retire at exact age 65 and so be treated as per the stanard age retirement situation when summing?
Answer to your first question: Because D62 and D60 use an interest rate of 4% but "superscript2A60" is an assurance with interest rate 8.16% I had the same problem
I'll have a go at your second question, although I'm not very good at pensions so don't know if my logic is right. Mx sums to 65 = NPA, so don't have a problem with that. With Mx'bar', it doesn't really 'sum' does it? Mx'bar' is just a Mx with the first half year bit taken away. The Mx'bar formula does include Mx, which does sum to 65, so Mx'bar' does include retirement at NPA. However, Mx'bar' is only valid at values of x<=64 because if x = 65, Mx'bar' would no longer make sense. So Mx'bar' does 'sum' to NPA, because Mx still sums to 65. However, Mx'bar' itself is not used at x = 65, which is why x<=64. Hope that make sense, or is correct...
In this example, C65 really should be defined separately, without the 1/2's on the subscripts. See defn on Page 21. You get an Mbar term when you consider each year of future service. See, for example, Pages 52 and 53. To get the EPV of the future service benefit, we add over all possible years of future service that would lead to accrual. In this case the last possible year of future service is the year of age (64,65). This gives us an Mbar(64) term. So to get Rbar, we sum up to 64.
