CM1 September 2023 Question 8i)

[Danny]

When working out the increasing term assurance needed for part i), the examiner report seems to suggest the formula for an increasing term assurance payable at the end of the year of death is:

(IA)^1_45:16=(IA)_45-v^15*_15p_45*(IA_60+15A_60-15).

However, the Acted formula provided in the handouts for an increasing term assurance payable at the end of the year of death is:

(IA)^1_x:n=(IA)_x-v^n * _np_x*((IA)_(x+n)+n(A_(x+n))

This means that in September 2023 question 8i), the implication is that an extra term, _15p_45*n needs to be deducted in order to calculate the increasing term assurance in this question.

To be clear, when I say _np_x I mean the probability that a life age x survives for n years. Apologies for the poor formatting!

Why has this been done? This leaves me really unsure as to what the actual formula is for an increasing term assurance.

 

[Joe Hook]

Hi,

You've written the formula (IA)^1_45:15=(IA)_45-v^15*_15p_45*(IA_60+15A_60-15) as though it's the value of the increasing term assurance but the examiners are actually calculating the value of the increasing endowment assurance there.

The value of an increasing endowment assurance is (IA):x - v^n * npx * ((IA):x+n + n*A:x) + n * v^n * npx. So, given we're using v^n and npx in the final two terms they can be combined together, and this is what the examiners have done.

Hope this helps.
Joe