SA3 mock 3 Q3 (2026 April)

[samiksha sindhu]

Hello,

I am struggling to understand the approach of the calculation shown in the marking scheme for mock 3 Q3. I have given my approach below , but it doesn't align with the solution. Could someone please explain how claim delays, policy exposure are calculated here for UPR and DAC calculations to get earned premium?

Earned Premium = Premium earned this year + Premium earned next year •

Product Y:
• Claim delay: 9 months
• Assuming on average policy incept in the start of the year and are annual
• On average claims are reported and settled after 9 months
• 3/12 or 0.25 of the written premium is earned in the year the policy incepts
• Thus: Earned premium from current year = 200,000*0.25 and Earned premium from next year = 200,000*1.1*0.75 . so, Total earned premium next year from product Y = 205,000
[why does the marking scheme not take the 9 month delay into account?]
Product X:
• Claims in the last quarter are twice the level of those in other quarters
C claims are reported and settled in first 3 quarters
2c claims are reported and settled in the last quarter
Total premium = 5P (P + P + P + 2P) Thus,
• Assuming on average policy incept in the start of the year and are annual
First quarter claims would be fully earned
Second quarter claims would be 3/4th earned Or 1/4th unearned
Third quarter claims would be 1/2 earned Or ½ unearned
Fourth quarter claims would be 1/4th earned Or 3/4th unearned
• Earned premium from current year: o 5P = 400 so P = 80 [Second quarter unearned = 20 , Third quarter unearned = 40 , Fourth quarter unearned =120 , Total = 180 ]
• Earned Premium for next year: o 5P = 400*1.05 = 420 so P = 84 [ First quarter earned = 84 , Second quarter earned = 63 , Third quarter earned = 42 , Fourth quarter earned = 42 , Total = 231]
• Total for product X = 411
[I don't understand how the quarterly table is created in the marking scheme]
Total = 411 + 205 = 616k

Can someone please breakdown the solution using basics?

 

[Katherine Young]

Claim delays have nothing to do with earned premium. The 9-month delay is irrelevant.

For Product Y we make the standard assumptions:
- business is written half way through the calendar period
- policies are annual
- risk is even throughout the policy term.

Hence, for product Y, earned premium b/f is 200*0.5=100, and earned premium c/f is 200*1.1*0.5=110.

For Product X, we carry out a similar calculation, but this time using the earnings pattern given in the first bullet point. We’re told: ‘for product X, claims in the last quarter of the year are twice the level of those in the other quarters.’

We’ll work in quarters, since that is how the information is presented:
- Policies written in Q1 are written half way through February, on average. So they will earn for half of Q1. Let’s call that ‘half a unit of risk’.
- They’ll also earn for the full quarter of Q2 and the full quarter of Q3. Let’s call that ‘a whole unit of risk’ in each quarter.
- But we’re told the risk is doubled during Q4. Let’s call that ‘two units of risk’.
- Since the average policy was written mid-February, it will remain on risk until mid-February of the following year. From 1st January to mid-February is only half a unit of risk in Q1 of the following year.

That gives us the first row of the table in the marking scheme. You should now be able to attempt the remaining rows of the table. Have another go and see how you get on.

To calculate DAC b/f, we use the golden rule: If acquisition costs are x% of WP, then DAC is x% of UPR. The fourth bullet point tells us that x=15%.

 

[Katherine Young]

Check out the student's question below. You can see it's not the first time the examiners have tested this.

I've answered the forum post, but have a go at it yourself before reading my answer. Now that you've understood your own question, this one should only take you a minute or two: https://www.acted.co.uk/forums/index.php?threads/april-2001-ques-4-403.20892/