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CT5 Part 5 Question 5.4

O

OmoT

Member
Please in the question/solution below, if the premium is a single premium, can someone explain why the premium of 8500 was included in the solution? The question says find the PV of the profit before the premium is paid.

Thank you.

Question:
A life insurance company sells a last survivor annuity of £500 pa to a man aged 65 and
a woman aged 70. The single premium for the policy is £8,500. The benefit is paid
annually in advance.
(i) Assuming that expenses can be ignored, write down a random variable that
represents the present value of the profit made on one of these policies, as at the
issue date of the policy, immediately before the premium is paid.

Answer:
upload_2017-8-30_21-0-44.png
 
Profit is equal to income minus outgo. We are looking at the future profit, from the moment just before the premium is paid.
So, the premium is part of our future profit at this point (because it hasn't been paid yet) and so it is included in the formula.
 
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