2025 Sept CM1B Q3(ii)(a) and 2023 Sept CM1A Q9(ii)(b)

[hyy]

edited

 

[hyy]

reposting my question due to formatting issues

I have some questions regarding the solutions of the exam questions.

in 2025 Sept CM1B Q3(ii)(a), question states to calculate reserves required at the end of each policy year.
my understanding is that reserves required at end of year t = prob of survival in year t * reserves required at the start of year t+1
my answer:

term	age at start of year	end of year cashflow	survival rates	reserves at start of year	interest	reserves at end of year	revised profit vector
1	40	55.07	0.9996	0	0	114.81	-59.74
2	41	-34.71	0.999463	114.86	3.45	83.59	0
3	42	-29.85	0.999122	83.64	2.51	56.29	0

however,the solution given did not multiply the reserves required by the probability of survival in the year, although this was done only when calculating the profit vector.
solution:

term	age at start of year	end of year cashflow	survival rates	reserve at end of year	revised cashflow
1	40	55.07	0.9996	114.86	-59.74
2	41	-34.71	0.999463	83.64	0
3	42	-29.85	0.999122	56.34	0

I encountered something similar in 2023 Sept CM1A Q9(ii)(b) as well.

may I know which answer should be given in the exam?

 

[AJ Vickersmith]

When reserves appear inside a profit test table, each row of the table is constructed on the assumption that the policy is in force at the start of that year. Because of this the reserve required at the end of the year must be multiplied by the probability that the policy survives through the year.

However, if the question simply asks for the reserve required at the end of a policy year, this refers to the reserve per policy still in force at that time. In that case, we do not need to multiply by the probability of survival, as we are calculating the reserve conditional on the policyholder being alive and in force.

Does that help?