MATH 3640 – Assignment 4
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1) (1.5 points) Given an annual premium trend of 10%, using one-step trending, what factor
should be applied to project Calendar Year 2022 Earned Premiums, assuming semi-annual
policies with a proposed rate effective date of 1/1/2025, where rates are expected to be in effect
for 2 years?
2) (1.75 points) Given an annual premium trend of 5%, using one-step trending, what factor
should be applied to project Policy Year 2022 Earned Premiums, assuming semi-annual policies
with a proposed rate effective date of 1/1/2025, where rates are expected to be in effect for 3
years?
3) (4.25 points) Given the following information, use two-step trending to calculate EPAPR at
prospective levels in total, for all historical years given:
 Semi-annual policies, written uniformly throughout the year
 Projected premium trend = 8%
 Proposed rate effective date is 7/1/2025
 Rates will be in effect for 1.5 years
Calendar Year EPAPR Avg EPAPR Avg On-Leveled WP
2020 5,000,000 4,900 5,000
2021 5,100,500 5,050 5,050
2022 5,500,000 5,150 5,100
2023 5,900,000 5,850 6,000
4) (5.5 points) Given the following information, use two-step trending to calculate EPAPR at
prospective levels in total, for all historical periods given:
 Semi-annual policies, written uniformly throughout the year
 Projected premium trend = 10%
 Proposed rate effective date is 10/1/2025
 Rates will be in effect for 2.5 years
Calendar Qtr EPAPR Avg EPAPR Avg On-Leveled WP
2022Q1 1,500,000 1,900 1,000
2022Q2 1,600,500 1,050 1,050
2022Q3 1,500,000 1,150 1,100
2022Q4 1,900,000 1,850 1,900
2023Q1 2,000,500 1,900 2,000
2023Q2 2,100,000 2,050 2,500
5) (1.75 points) Calculate the factor to be applied to Accident Year 2022 historical losses to trend
them to the prospective period:
 1.5% annual loss trend
 Semi-Annual policies
 Proposed rate effective date: 4/1/2025
 Rates will be in effect for 1.5 years
6) (2.75 points) Given the following information, calculate the Adjustment Factor for
3Q2023 AY Losses:
 A change was implemented on 4/1/2023 that only affects losses on policies written on or
after 4/1/2023. The direct effect of the change for semi-annual policies on an accident
year basis is estimated at +10%.
 Another change was implemented on 7/1/2023 that affects losses on policies currently
in-force at the time. The direct effect of the change for semi-annual policies on accident
year basis is estimated at -5%.
7) (2.5 points) Assuming a 15% ground-up loss trend and a $10,000 limit, calculate the impact on
the excess layer using the following claims’ total limits losses:
Claim Number Total Limits Loss (Ground-up Loss)
123456 8,000
123457 12,500
123458 9,500
123459 8,000
123460 10,500
123461 13,200