Chapter 5, reserves

Hi,
Firstly thank you for taking out some time and viewing this question.

1.) I'm stuck on this question for a while now. It's question 5.11 on page 22. The thing I couldn't understand was the answer given in the solution section of that chapter. To be more precise I want someone to explain me,
Why will the insurer make a loss from having the contract sold?

2.) I've a second question as well. The question is from the same chapter, but from section 5.1, it talks about 'retrospective accumulation of benefits'
what does "retrospective accumulation of benefits" exactly mean?

P.S.: I've attached the required docs.

 

The insurance company will break even under the contract if it receives all the premiums it expects and pays all the claims it expects, according to the assumptions it has made about mortality, interest, etc. So this will happen if the policyholder keeps paying premiums until the end of the term (or dies earlier, of course).

If the policyholder stops paying premiums (so the contract lapses) then the expected future premiums, and the expected future claims, will not occur. As the value of the future premiums is greater than the value of the future claims (in this case) then the company loses more money (in lost premiums) than it gains (from not having to pay those claims). And so it will make an overall loss on the contract.

The "benefit" is just the payment made under the policy when it becomes a claim. so in the case of the pure endowment, the benefit is paid at the maturity date, so the payment earns no interest from the time it is paid until the accumulation date! Also, it is by definition only paid to someone who survives, so the "accumulated amount of this benefit per survivor" is just the benefit amount. (ie this is a trivial example). A more revealing example is the term assurance "benefit" (sum assured) shown in Section 5.2. There is another recent thread on this forum where this is discussed - have a look at that also. But please don't worry too much about the theory on this section, all you really need to be able to do is to calculate a retrospective accumulation.

 

Thank you