IP Claim Inception & Disability Annuity Approach

Hi

I'm a bit confused with the example on page 22 chapter 16. The details are:

The policy has a deferred period = 1 year, pays £25000 pa for the first year of sickness and £15000 pa for all subsequent periods. The question asks for the expected claims costs in the 4th and 5th years. In the solution, the first part of the formula calculates the EPV of the £20000 benefit but then the second part of the formula subtracts a benefit of £10000. Subtracting this second annuity then leaves us with the EPV of the £15000 benefit commencing one year later. Isn't this solution calculating the EPV of all the benefits until age 65 instead of calculating the expected claims cost in ONE YEAR?

If anyone could help, I'd appreciate it. Thanks!

 

The formula shown under the solution on page 22 is a general formula applicable for any years 0, 1, 2, 3, and so on.

EPV of all benefits, which you mentioned, can be calculated if you put a sigma sign in front of the formula with t starting from 0 to limiting age.

For expected claims cost in years 4 and 5, you simply need to plug in t = 3 and t = 4 in the formula and add the two results together. That is what has been done in the solution in the paragraph immediately below the general formula on the same page.

Anyway, the general formula is [sum assured x survival factor x claim inception rate x annuity x present value factor] for the expected claims cost. I think that for any inception/annuity calculation approach required in the exam, you should be able to get a significant number of marks if you include these 5 factors even if you make some mistakes.

 

Thanks for your help.

So if I plug in t=3 then I get the EPV at age 33.5 of:
(benefit of £20000 payable between ages 33.5 and 34.5) + (benefit of £15000 payable between ages 34.5 and 65)
So in asking for "the expected claim cost in the 4th year", are they just asking for the EPV in that year of all future benefits?