This notation is baffling me and I can't learn it as every question seems different. I wrote down that A30:25 with a 1 above the 30 is: A30 - D55/D30 times A55 Then I do a question in a past paper (Q12 of Apr 08) and the answers imply thay A30:25 with a 1 above the 30 would be: A30:25 - D55/D30 I then thought "I wonder if these are the same and it's just different notation" and it turns out I get different answers. Could someone explain why they are different please? I'm using ASET and they don't explain the notation well, and sometimes they use the D function then others they use v to the power of and it gets confusing. They should add notes to things like this when they change their usual way of writing it.
The first assurance function (with 1 above 55) is always equal to A30 - D55/D30*A55 The Other assurance function , which is equal to A30 - D55/D30 is true in case of Endowment Assurance contract only. Note that D55/D30 is actually EPV of a pure endowment contract for life aged 30 now, term being 25 yeras. Also note that EPV of Endowment Assurance contract = EPV term assurance contract of term n years + EPV Pure Endowment assurance Contract of term n years. Basically, the answer given in the paper is wrong!
Hmm now I'm confused because I see where they've got their expression from based on your last equation....but this doesn't match up with what I had written down so it doesn't make sense. Can you really just mix together assurances?
Wouldn't go as far as to say it's wrong. (It's correct within the scope for difference of interpretation of notation in post etc.) D55/D30 is a pure endownment at age 30 with benefit at age 55. I read the first as Term life from 30 to 55 = whole of life at age 30 less pure endowment at age 30 with benefit equal to a whole of life from 55. Latter is simply a discounted (delayed) whole of life. This is correct. I read the second as Endowment (ie death and survival benefits) at age 30 term 25 years = term assurance (age 30 term 25) less pure endowment which is also correct. (Full) endowment has no 1. Term has 1 over age. Pure Endowment has 1 over term. It's all a matter of working with what you have to get what you want. You don't always have access to everything you need to do it the exact same way every time.
How different? Are you sure that underlying assumptions are same in both questions, eg discount rate, mortality? Are you picking up correct figures? Could be rounding?
Man...no idea what I did wrong but I now get the same answer. That at least makes me more comfortable even if I still am nowhere near to understanding the notation. Cheers folks.
Hey Sorry I wrote some parts which were incorrect. Actually, A30:25 - D55/D30 is same as A30:25(with 1 above 30). A30:25 is the EPV of endowment assurance, and D55/D30 is the EPV of pure Endowment of same term. Hence differenceof two is always EPV of term assurance. As expected , you should get same answer from both the approaches..
Basic rules of thumb: 1. D functions when working with a rate of interest of 4% otherwise use v to the power of. 2. When working out term assurances and x+n= 60 or 65 use the (endowment assurance - Pure endowment) approach otherwise use whole life assurance functions.i.e A_n-v^n*nPx*A_x+n
