1. **Problem Statement:** Calculate the average profit or loss percentage for the reinsurer under a 20% commission treaty based on the given yearly premiums and claims. 2. **Formula and Explanation:** The reinsurer's profit or loss for each year is calculated as: $$\text{Profit} = \text{Premium Earned} - \text{Claims Incurred} - \text{Commission}$$ where commission is 20% of the premium earned: $$\text{Commission} = 0.20 \times \text{Premium Earned}$$ The profit percentage is: $$\text{Profit \%} = \frac{\text{Profit}}{\text{Premium Earned}} \times 100$$ 3. **Calculate yearly profit:** For each year, calculate: $$\text{Profit} = \text{Premium Earned} - \text{Claims Incurred} - 0.20 \times \text{Premium Earned} = 0.80 \times \text{Premium Earned} - \text{Claims Incurred}$$ 4. **Calculate yearly profit percentages:** Calculate: $$\text{Profit \%} = \frac{0.80 \times \text{Premium Earned} - \text{Claims Incurred}}{\text{Premium Earned}} \times 100 = (0.80 - \frac{\text{Claims Incurred}}{\text{Premium Earned}}) \times 100$$ 5. **Calculate for each year:** - 2005: $0.80 - \frac{550470}{642481} = 0.80 - 0.8569 = -0.0569 \Rightarrow -5.69\%$ - 2006: $0.80 - \frac{825036}{1144000} = 0.80 - 0.7213 = 0.0787 \Rightarrow 7.87\%$ - 2007: $0.80 - \frac{1225000}{1444284} = 0.80 - 0.8483 = -0.0483 \Rightarrow -4.83\%$ - 2008: $0.80 - \frac{1260850}{1714452} = 0.80 - 0.7359 = 0.0641 \Rightarrow 6.41\%$ - 2009: $0.80 - \frac{1765492}{2404722} = 0.80 - 0.7343 = 0.0657 \Rightarrow 6.57\%$ - 2010: $0.80 - \frac{1938017}{2648881} = 0.80 - 0.7315 = 0.0685 \Rightarrow 6.85\%$ - 2011: $0.80 - \frac{3125620}{3056737} = 0.80 - 1.0221 = -0.2221 \Rightarrow -22.21\%$ - 2012: $0.80 - \frac{1915292}{3408859} = 0.80 - 0.5617 = 0.2383 \Rightarrow 23.83\%$ - 2013: $0.80 - \frac{3420876}{4704985} = 0.80 - 0.7275 = 0.0725 \Rightarrow 7.25\%$ - 2014: $0.80 - \frac{6394562}{6874715} = 0.80 - 0.9300 = -0.1300 \Rightarrow -13.00\%$ 6. **Calculate average profit percentage:** $$\text{Average} = \frac{-5.69 + 7.87 - 4.83 + 6.41 + 6.57 + 6.85 - 22.21 + 23.83 + 7.25 - 13.00}{10} = \frac{13.05}{10} = 1.305\%$$ 7. **Conclusion:** The average profit percentage for the reinsurer is approximately 1.3%, which is greater than 0% but less than 5% profit. **Answer:** B. The treaty on average produces results for the reinsurer in excess of 0% but less than 5% profit