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Life Assurance
Saturday, September 1, 2007
Fancy figures

An actuary might tell you that a man aged 36 next birthday has to pay R14,27 per month per R10 000 of basic life cover. Sounds quite scien¬tific. It’s worked out using the mortal¬ity tables, a few assumptions about interest rates and ex¬penses, and reserve ac¬cumulations.
Supposing the number of 15-year olds who will survive to 50 years old is 914 359. Thus, the probability of a person aged 15 surviving to 50 is 914 359 divided by l million, or 0,914.


The mortality tables indicate how many will die in each year of life. In fact they go up to 111 years when 0,54 of the original l million people are still supposed to be alive! But that’s extrapolated graphs and statistics for you.
Starting with one million people aged 15, the mor¬tality tables indicate that 998 579 will survive to 16. In other words, 1 421 will die. The accompanying table shows how life premiums are calculated for a person aged 16 next birthday.
For our simplified example, we’ve used a one-year term policy for a sum assured of R10 000. It works out at R20,44 per year, or less than R2 per month per R10 000 of basic life cover. Since we know that 1 421 people will have died during the year before reaching the age of 16, we can calcu¬late that each of the original one million people will have to pay R14,20 during the year to cover the claims of R10 000 each (see part 1).
Part 2 of the calculation brings interest into the picture at an as¬sumed rate of 12% per annum. Since, on average all the claims will be paid out half way through the year, it fol¬lows that 6% interest is earned on the total contributions. Total premiums are 100% then, plus the 6%, giving a factor of 1,06.
Finally, commissions must be grossed up, say, by 10% (or R2,04); and a policy fee must be added as an average expense per policy regard¬less of premium amount (say R5). Thus bringing total premium to R20,44 for the year.
For subsequent years the calcula¬tions are compounded and an annual or monthly flat premium deduced for the whole period. The basic premium attaches to the ‘standard policy wording’.
For ‘non-standard’ lives the ac¬tuary might decide to determine ex¬clusions, a limit on benefits, a loading of premium or a mixed package of such conditions, depending on the circumstances, the precise nature of risk and the type of life assurance being proposed.

 

Copyright © Insurance Times and Investments® Vol:20.8 1st September, 2007
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