Review questions

[Jo_Jo]

could you please help with the following questions:
1. chapter 3 P33 Example
why q47 = 0.001415 but not 0.001018?
2. 2006 Apr Q13
for claims expenses $150 on maturity, why use negative when calculate
the expenses?
3. Assignment 3 question 3.12 solution on page17 (iii)
i understand how to calculate cost of "increasing reserves" but don't know how to calculate "profit ignoring reserves" and "profit allowing for reserves"

4. chaper14 P38 Q14.17
pls explain how to deal with max of 2/3 of final pensionable salary? and why just C ra 65?

 

[Mark Mitchell]

Points in turn:

1. q[47] = 0.001018; q47 = 0.001415. The difference between these is the difference between select and ultimate mortality. The ultimate mortality is what we have when the effect of the selection process has worn off - here that's after 2 years, so the final column is the ultimate mortality you need.

2. The first term in the EPV of expenses expression uses an endowment assurance, so this incorporates a payment of 300 on death or survival. We need expenses of 300 on death (covered correctly by the first term), but only 150 on survival. Hence the subtraction of 150 (to get us down from 300 to 150) multiplied by a pure endowment factor, to cover survival expenses.

3. Profit ignoring reserves is as calculated in ii) - it's the final column of the second table on page 16. Profit allowing for reserves = Profit ignoring reserves - cost of increasing reserves.

4. It's just Cra65 because the retirement pension is only payable on retirement at age 65 in this question i.e. no "early retirement" is allowed, so the only rx (where rx = number of retirements aged x) that is not zero is r65.

The maximum pension of two thirds of final pensionable salary is used to calculate the pension that will be received at age 65. Since the member has 14 years past service and will accrue 18 more years between now (age 47) and 65, this gives 32 years service. This exceeds the maximum of 2/3 (=30/45). So we just value 2/3 of final pensionable salary. (There's more on this type of limits on service idea in the example on page 27 of chapter 14.)