1. **Problem Statement:** The Intrepid Insurance Company writes 25% of a risk with a sum insured of 4,000,000. It has an 80% quota share treaty, a gross retention of 500,000, and a 5 line surplus treaty. We need to determine which statement among A, B, and C is correct. 2. **Understanding the terms:** - Written risk by Intrepid: 25% of 4,000,000 = $1,000,000$ - Quota share treaty means Intrepid cedes 80% of its written risk to reinsurers and retains 20%. - Gross retention is the amount Intrepid retains before surplus treaty applies. - Surplus treaty allows Intrepid to cede amounts above its retention in lines (here 5 lines means Intrepid can retain up to $5 \times 500,000 = 2,500,000$ before ceding surplus). 3. **Calculate Intrepid's net retention after quota share:** $$\text{Net retention after quota share} = 20\% \times 1,000,000 = 200,000$$ 4. **Check if surplus treaty applies:** - Intrepid's retention limit = $5 \times 500,000 = 2,500,000$ - Written risk = 1,000,000 which is less than 2,500,000, so no surplus cession is needed. 5. **Final net retention:** - Intrepid retains $200,000$ after quota share. 6. **Check the statements:** - A. Intrepid retains net 400,000. (Incorrect, actual retention is 200,000) - B. Intrepid cedes 2,500,000 to surplus reinsurers. (Incorrect, no surplus cession since risk is below retention limit) - C. Intrepid cedes 40% to quota share reinsurers. (Incorrect, cession is 80%) **Answer:** None of the statements A, B, or C is correct based on the given data.