CAS Exam 5 Spring 2018, Question 9
Study guide: Exam 5
Given the following information for two personal automobile policies:
Three-Year Time Horizon for 21 Year-old Driver
| Year | Age | Premium ($) | Loss ($) | Expense ($) | Renewal Probability |
|---|---|---|---|---|---|
| 1 | 21 | 1,215 | 1,200 | 50 | |
| 2 | 22 | 1,200 | 1,125 | 20 | 75% |
| 3 | 23 | 1,185 | 1,050 | 20 | 75% |
| Total | 3,600 | 3,375 | 90 |
Three-Year Time Horizon for 65 Year-old Driver
| Year | Age | Premium ($) | Loss ($) | Expense ($) | Renewal Probability |
|---|---|---|---|---|---|
| 1 | 65 | 900 | 795 | 50 | |
| 2 | 66 | 900 | 839 | 20 | 95% |
| 3 | 67 | 900 | 859 | 20 | 95% |
| Total | 2,700 | 2,493 | 90 |
| 5% | Annual discount rate |
- Policies are written on January 1.
- Premium is collected and the expense and losses are incurred on January 1.
Evaluate whether the 21 year-old or 65 year-old has a larger percentage return on premium over the three-year horizon.
Part a (1.75 points)
Answer this question and see the worked solution