Q&A Bank, Part3, Solution 3.23 (ii) Revised profit

[ActStudent]

Does anyone know why there's a difference between the reserve for start of year 3 and end of year 2?

I'm quite lost with the table below too. Could anyone kindly tell me the formula in each cell? Especially the "Increase in reserves" column?

Thanks!

 

[Louisa]

Okay, working it out from their calculation, it looks like their "end of year 2" figure differs because
- it is calculated per policy in force at the start of year 2
- it is calculated to zeroise end-of-yr-2 profits.

If i've got that right I find it rather confusing though, as usually we calculate reserves at the end of the year per policy in force at the end of the year.

Let t_V be reserve set up at the end of year t (or beginning of year t+1 in Acted's notation) per policy in force at the end of year t. (= "Non-unit reserve bf" I think)
Then the formulae are
(1+i)*{t-1}_V = p_{40+t-1} * t_V (+ loss at the end of the t'th year if any)
i.e. 1.05 {t-1}_V = .99 t_V (+ loss if any)
(Because reserve at beginning of year t after interest needs to give us enough to set up reserve at the end of the year for those policies which are still in force, and the expected loss at the end of year t to zeroise the losses.)

Increase in reserves = 0.99 t_V - {t-1}_V
Interest on reserves = 0.05 * {t-1}_V
(increase in reserves is sometimes different when we incorporate the interest into the increase in reserves)

And profit allowing for reserves
= profit ignoring reserves
+ interest on reserves
- increase in reserves