Could anyone please help me with this qus.? Qus. A whole life increasing annuity-due is issued to a life aged 65. The first annual annuity payment is £5000 and this increases by £500 pa. Initial expenses are £250 and renewal expenses are 1% of each annuity payment including the first. i)Calculate the gross premium reserve at time 10 assuming AM92 ultimate mortality and 4% pa interest. ii) Use recursive formula for gross premium reserve to calculate the reserve at time 11. Ans. (i) £110670 (ii) (10V - b10 - e10)(1+i) = 11V p75 where b10 is benefit payable at time 10. I didn't get part(ii). How the recursive formula is used here? Why they subtracted b10 and then accumulate the reserve in LHS? Could anyone please explain? Many thanks in advance.
Sir, it is from Revision notes, chapter-6,7 booklet, practice qus.16. There was a problem in uploading the file, so I typed the question here. I just didn't get the b10 in the recursive formula, it would be great if you can help me out. Thankyou
The reserve at time 10 is the pot of money that the company has for this policy at the very start of year 11. The recursive formula starts with this reserve amount, then adds in all the expected cash inflows during the year, and deducts all the expected cash outflows during the year. This is an annuity policy, so the annuity benefits form a cash outflow every time they are paid. And because this is an annuity due, then the next annuity payment occurs straight away at the start of year 11. This amount (b10) then has to be deducted from the reserve at the start of the year before any interest can accrue on the amounts invested. Robert
Hi Robert, Thanks for explaining annuity due. Please confirm one more thing for Annuity arreer: What I understood in case of Annuity arrears we only take anuuity payment of that time only for in force policy in RHS becoz annuity doesn't have death benefit. Is it correct ? Sunil
Hi Sunil - I think we're not on the relevant thread here, so I've lost the context of your question and so I don't quite follow what you're asking, apologies. Please can you clarify what you mean? Thank you! Robert
Hello sir. He is asking a thing relevant to my thread only. You have explained the recursive formula in case of annuity due. He wants you to confirm this in case of annuity in arrear. Should the recursive formula be like this: (tV + P)(1+i) = px+t(t+1V + R ). If there is no death benefit since it is an annuity. And because of annuity in arrear, we are taking R on RHS instead of LHS as in case of annuity due. Could you please check once ? Thankyou
