http://www.actuaries.org.uk/__data/assets/pdf_file/0006/166326/ExamPapersSubject102_2000-2004.pdf (PAGE 48/164 in the PDF) Q6) Where do you get the interquartile range for N(0,1) being -0.674 abd 0.674 from? I don't really understand what I have to do with this question. Will I need to know how to calculate the interquartile range? Q8) Is this not a very harsh question?! How do I find the first guess for the equation? I managed to form the equation using the PV of income and outgo but I couldn't find a first guess so I skipped it Q12c) When finding the DMT with v^10*annuity payable in arrears for 10 years why is the DMT Ia (arrears for 20 years) - Ia (arrears for 10 years)? Sorry my questions are a bit brief, I did this paper a bit ago and I can't quite remember precisely what I didn't understand. Thank you for your help.
6) I don't know if the statistics knowledge required is still examinable or assumed for CT1. Basically, you have the distribution and the interquartile range is the upper quartile less the lower quartile. Where the quartiles are the values x for which P(X<x)=0.25,0.75. 8) Whilst an educated guess is likely to help, it's still a guess after all, so if all else fails make something up (10% works well in almost every example as returns are generally between 0 and 20-30%pa) and see how wrong, and in which direction, it is? General principles are to make it simple - ie don't need to solve anything more complicated than linear equation, or quadratic at most. if there is a large once off payment, then it would help if you treat it correctly treating annuities as a once off payment of the total (possibly approximate) amount at the middle of the payment period. Coincidentally (or not) this is what the examiners did. Outgo = 1000 (At start) + 44*20 v^10 (average amount of 44 for 20 years on average at t=10) Income = 200*(1.03)^9*20 v^10 Ignoring the first payment (and last payment so that we have an even number), the others are on average 200*(1.03)^9. OK the arithmetic average isn't the same as the geometric but it's close enough for these purposes. The first payment is a little more than half than the corresponding payment in the first year if you follow the pattern, ie 200/1.03 - not worth the extra complexity. so we just treat it as 20 payments of 200*(1.03)^9 v^10. If you really wanted you could maybe knock off 94 or so at the start to make up for the differing first payment. I doubt that different approaches would have made a difference, eg using 1.03^10 instead, knocking off the 94. Bottom line, use the approximations above, but always remember that you could use straight guessing - plug in 10%,20% etc then narrow it down to 5% ranges , then 1% ranges etc. Use whichever you feel will use less time, and since it is a broad guess you could ignore specifics like payable monthly, weekly etc until the finer tuning. 12) DMT is amount paid * discount * time. so after time 10 (since this is when cashflows change), we have 11*v^11 + 12*v^12+...+ 20v^20 (times the annual cashflow) That's all it is. However, it's nice to use the precalculated amounts when you can (unless you like adding up 20+ numbers) so you rewrite it (Ia)20 -(Ia)10 = (v+2v^2+...20v^20) - (v+2v^2+...+10v^10) ie what we want. Alternatively, could use v^10 ( 10* a 10 +(Ia)10)
