Hi, I have a few questions: 1. Mock 2023 Paper A /13. what does the sentence"die at an employee at 41 last birthday" mean? What is meant by independent force (I can only find independent prob)? 2. Tutorial Paper B handout /9. (d) Paid after first death until 5 years after second death I tried to work out the assurance using premium conversion formula: =1-0.035/1.035*(aLS+1)= 0.0787143 ==> What have I done wrong?
3. CM1A 2021 Sep /11 iv why is the sum assured at t=5 s*1.05^5 rather than 1.05^4? (am I confusing it with what the policy holder actually gets ie if they die in year 4 then they gets 4 increases)
1. This means the probability that they die from the active state between age 41 and 42. It's not the probability they simply die because the life could transition to the withdrawal state and then subsequently die. Here we are only interested in them remaining active (employed) to age 41 and then dying from the active (employed) state between 41 and 42. The independent force is just the force of transition. However, you will see it referred to as an independent force throughout the in-chapter questions of chapter 24. 2. Take prob of payment each year on the last survivor annuity and multiply by relevant discount factor. If you sum those values up you get 16.65649. Add 1 to this and you get 17.65649. 1 - (0.035/1.035)*17.65649 = 0.4029205. This is equal to the value of the assurance factor that we're looking for. 3. I think you're thinking is right here. The sum assured in the 5th year will be s*1.05^4 but then once we hit time 5 and if the life has survived the sum assured will not be s*1.05^5 and if they die in the 6th year this is what they will receive. Joe
A few more questions: 4. Is it right that the premium conversion formula only applies to EA but not TA? 5. Haven't seen any super compound with profit policies in the exams, but is this examinable? 6. Have seen Joint Life Mortality Profit Question first, but is this still examinable? (i guess both answers are "yes, though not likely"). I have also seen Joint Life reserves in the assignment.
Hi, 4. That is correct 5. Potentially, but if they do examine I would expect them to spell out the benefits fairly clearly. They may choose to do it in paper B where you can project the cashflows in Excel. 6. Yes, still examinable. As you say it is unlikely (based on 1 question in the last 10 years).
Thank you 7. on 2020 Sep Paper B/1. the solution calculated P(death in month t). I tried to calculate t-1|q70 = t-1p70*qx giving 0.001042372 0.002081485 0.003114099 0.003104371 0.004119782 0.005120275 0.006102822 0.007064489 0.008002452 0.00891401 0.009796595 0.010647792 where my t-1p70 1 0.998958 0.996876 0.993762 0.989625 0.984478 0.978337 0.971221 0.963151 0.954153 0.944254 0.933483 what has gone wrong?
Hi all, i have a question on examiner's allowance for differences vs model answer. For example - i refer to the CMP Chapter 22, on page 36. CMP answer is $1,566, but my excel formulas come up with $1,564 as i used the actual numbers in the excel (with multiple decimals). Will I be penalized for not having the same answer as the examiner, or do I get the full marks as well if I can show the workings?
Hi Chun, You will likely receive full marks for the accurate answer (ie using actual numbers in excel as you have done above) or for using a sensible amount of rounding. Kind regards, Richie
Hi all, got a question here again. On chapter 7 level annuities practice questions For example for 7.4 & 7.6 where payments are per month, we use monthly effective interest rate. But for 7.7 we use interest rate convertible quarterly. Would like to get some guidance on when should we use effective vs convertible rates please. For example - for q7.7, how do we tell we need to use convertible quarterly rates, rather than quarterly effective rates.
Hi Chun, There are often several possible approaches, and the solutions use a variety of these to demonstrate the alternatives. Some solutions, including those you quote, even demonstrate multiple approaches to the same question. For example, Question 7.6 initially calculates the answer using annual annuities convertible monthly, and hence the rate convertible monthly is needed for the calculation. But it then also calculates the answer using monthly annuities, ie where the term is the number of months rather than years, and hence the monthly effective rate of interest is needed instead. I'd suggest trying each to see which you find most straightforward or logical. For the avoidance of doubt, the approach taken to calculate the rate needs to be consistent with the approach taken for the annuities. Eg if you are using annual annuities you need an annual effective rate. If you are using annual annuities convertible pthly, you need to use the annual rate convertible pthly. And if you are using monthly (or quarterly annuities), ie where the term is the number of months (or quarters), you need to use the monthly (or quarterly) effective rate. Thanks, Richie
Hi Richie, thanks for this. I have one question on 27.5 Reserving, in the solutions it shows Expected Cost of increase in reserves for y1, y2 and y3 as -0.9920P, 0.0790P and 1.07P. I am stuck here for like 15 minutes, and i need some guidance please
Hi, The cost of increase in reserves = {probability of staying in force over the year} x {reserve per policy at end of year} - {reserve at start of year} – {interest on start year reserve} The questions says that the reserves = One year’s office premium. The reserve at the start and end of contract is zero and at all other time points the reserve per policy is the unknown premium we need to solve for, P. The probability of staying in force (i.e. not dying) from the start of year 1 to the end of year 1 = 1 - q60 = 1 – 0.008022 = 0.991978 The probability of staying in force from the start of year 2 to the end of year 2 = 1 - q61 = 1 – 0.009009 = 0.990991 The interest on the start year reserve in year 1 is 0 because the reserve at the start of year 1 is 0. The interest on the start year reserve is years 2 and 3 is 0.07P i.e. 7% investment return on the reserve. Putting this all together Hope helpful, Michael
