Assignment X3, Question X3.6

[corpact90]

Hi everyone, I have a doubt related to the solution of the question X3.6.
In the section where the expenses are calculated, I don't understand why they are discounted by three months.
The question said that expenses are initially £1 per month throughout the life of the policy and paid 9 months after inception.
Now if we considered that for a policy starting on 01/01/2016 the expenses would be 1*12=12, if the policy starts on the 01/07/2016 (mid year), this value would be 12*1.01^6= 12.74. Interest rate is 1%.
Now this amount would be paid 9 months after this time, so at the inception, 01/07/2016 the expenses should be 12.74*1.01^(-9).
What I don't understand is that in the solution this value is discounted for three months only as the expenses are paid 9 months after 01/01/2016.
Why is that?
Thank you very much for your help

 

[Hemant Rupani]

From point (n)
"Assume all claims and per policy expenses are paid 9 months after inception."

 

[corpact90]

That's why I don't understand, in all the calculations it is assumed that the policy is incepted at 01/07/2016 which is the mid-year point. In this case the expenses will be paid at 01/04/2017, 9 months after. The amount should therefore be 12.74, which is £1 per month accumulated six months to get to 01/07/2016, when the policy starts, discounted 9 months. Why do they do only three?

 

[Hemant Rupani]

12.74 is the inflated at inception.
& For overall year, expected average date is 6 months.
So payments 12.74*1.01^6 is inflated at occurance date, but payment date is different.

We know, Inflation applies upto occurrance date and discount factor applies upto payment date

So answer 12.74*1.01^6*1.01^(-9)

 

[corpact90]

Thanks, just a question, what do you mean with expected average date is 6 months?

 

[Hemant Rupani]

Expected average date for payments.
As payments are made after 1,2,...12 months, average 6.

Well, I know answer is very naive.

 

[corpact90]

All clear, thanks