Quote:
Originally Posted by Lombard4902
Can anyone walk me through the solution for #1 on Exam 5, Fall 2019? Need help understanding even with examiner's report lol. Parts a, c, and d.

I can try to explain how I think the examiner's report arrived at their answer. Let me know if you need me to explain anything further.
For part a they want 2017 policy year earned exposures as of March 31, 2018. According to the problem the quarterly earning pattern is not uniform but it does follow a pattern. For the 1Q we know that 5% of the premium written in 1Q will be earned in the 1Q because for 2017Q1 we earned 5 earned exposures (EE) and we wrote 100 written premium (WP), 5/100 = 0.05. At March 31, 2018 we know that all the EE earned in 2017 are from the 2017 policy year, but for 1Q2018, some of the EE are coming from 2018Q1 WP. Since we know that 5% of the WP for 2018Q1 is earned in 2018Q1 so we do 5 + 247.5 + 427.5 + 52.5 +53.75  125 * .05 = 780.
For part b they want the inforce exposures as of May 31, 2018. We know that all policies are written on the first day of the quarter. We also know that by the end of 2018Q1 all the written policies in 2017Q1 and 2017Q2 will have been fully earned. So we sum up the written exposures from 2017Q3 to 2018Q2 to get the number of policies that could still be active. 400 + 100 + 125 + 550 = 1175.
For part c they want the 2018 calendar year unearned exposures. Since the business started writing on 1/1/2017 and stopped writing on 12/31/2018, and assuming they want the unearned exposures past the date of 12/31/2018 since they didn't give us an asof date, we can simply add up the WP column and subtract the EE column. Since the company only wrote business for 2017 and 2018 and all policies are annual, by the end of 2018Q3 all the 2017 WP should have been earned. That just leaves 2018 WP left to be earned.
For part d they want the 2019Q1 earned exposures. We know that 5% of the WP in the Q1 is earned in Q1. For 2019Q1 we are only earning premium from the 2018Q2, 2018Q3, and 2018Q4, since we didn't write any new business in 2019 and by 12/31/2018 all the WP in 2018Q1 will have been earned. Likewise, we know that for 2018Q1, 5% of the WP for 2018Q1 was earned and the rest came from the 2017 policy year. So what we can do is take the 2018Q1 EE, 53.75, subtract 5% of the WP for 2018Q1, 53.75  0.05 * 125 = 47.5, and divide it by the sum of the WP for 2017Q2 through 2017Q4, 47.5/(450 + 400 + 100) = 0.05, to get the percentage of earned premium in 1Q2018 for written premium in 2Q2017 through 4Q2017. Then we just take 0.05 we just found and multiply that number by the written premium in 2Q2018 through 4Q2018 to get the earned premium for 1Q2019, 0.05 * (550 + 475 + 30) = 52.75.
Let me know if I need to clarify anything.