MATH 3640 – Assignment 3
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1) (2 points) Given the policy data below:
i. Calculate calendar year 2021 written premium as of 12/31/2021
ii. Calculate policy year 2021 earned premium as of 12/31/2021
2) (2 points) In your own words, describe what is meant by the following:
i. An exposure base should be directly proportional to expected loss
ii. An exposure base should be practical
3) (1 point) In addition to the two properties given in #2, describe one additional ideal property of
an exposure base.
4) (1.5 points) Describe the Fundamental Insurance Equation and fully explain two key points to
achieve the appropriate balance of the equation.
5) (2.5 points) Describe the purpose of adjusting historical premiums for ratemaking and explain
each of the three adjustments typically made.
6) (4.5 points) Using the following information, calculate the on-level factor to be applied to the
2022 Calendar Year Earned Premium in order to bring it to current rate level:
 Semi-annual policies, assuming uniform writing throughout the year
 Rate increase of 5% on 7/1/2021
 Rate decrease of 10% on 10/1/2021
 Rate increase of 8% on 4/1/2022
 Rate increase of 12% on 10/1/2022
 Rate decrease of 9% on 4/1/2023
Policy Effective Date Expiration Date Premium
1 6/1/2020 5/31/2021 490
2 7/1/2020 12/31/2020 130
3 3/1/2021 2/28/2022 220
4 8/1/2021 1/31/2022 310
7) (5.5 points) Calculate the 2022 Calendar Year Earned Premium on-level factor, using the
information given in #6, as well as a law-mandated decrease of 6% on all in-force policies as of
7/1/2022.
8) (1 point) Briefly describe two problems associated with using the Parallelogram Method.
9) (5 points) Given the policy data below, calculate the earned premium for calendar year 2021.
Assume that premium is earned at twice the rate in the first quarter of the year (January,
February, and March) versus the rest of the year.
Policy Effective Date Expiration Date Premium
A 10/1/2020 9/30/2021 1000
B 9/30/2021 3/31/2022 500
C 4/1/2021 3/31/2022 100
D 1/1/2021 12/31/2021 200