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CT5 part2 Q&A Question 2.28

M

ML Actuary

Member
The question:
A whole life assurance policy pays a benefit of 50,000 at the end of the year of death. The policyholder is currently aged 30 and is paying annual premium of 700 at the START of each year. A premium just been paid.

My question:
When we calculate the loss function why do we used an annuity arrears formula with K30 instead of annuity in advance with K31? Is it because of the last statement in the question, or is it we wanted to make the loss a function of K30? Do we ignore the fact that the premium is paid at the start of the year and the very 1st premium?

Thanks.
 
Hi, the line below probability equation will help you.
"noting that the next premium is due in one year’s time, hence we use the annuity function for payments in arrears."
2) Do not confuse with notations. \(K_{30}\) and \(K_{30}+1\) are different, latter is not equal to \(K_{31}\)
for assurance function if benefit is paid @ year end then \(K_x + 1\) will be duration.
For annuity if it due then \(K_x + 1\) and for arrears \(K_x \)
 
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