Trust Insurance Company has a surplus-share treaty with SwissRe Reinsurance. Trust has a retention limit of \( \$ 200,000 \) (one line), and four lines of insurance are ceded to SwissRe. How much will SwissRe pay if a \( \$ 400,000 \) building insured by Trust suffers an \( \$ 200,000 \) loss?

To solve this problem, we need to determine how much SwissRe will pay for the loss based on the surplus-share treaty between Trust Insurance Company and SwissRe. ### Known Conditions: 1. **Retention Limit of Trust**: \( R = 200,000 \) 2. **Total Insurance Amount**: \( T = 400,000 \) 3. **Loss Amount**: \( L = 200,000 \) 4. **Lines of Insurance Ceded to SwissRe**: 4 lines ### Step-by-Step Solution: 1. **Determine the Amount Retained by Trust**: Trust will retain the first \( R = 200,000 \) of the loss. 2. **Calculate the Loss Amount Exceeding Retention**: The total loss is \( L = 200,000 \). Since this loss is equal to the retention limit, Trust will cover the entire loss up to its retention limit. 3. **Determine the Amount Ceded to SwissRe**: Since the loss does not exceed the retention limit, there is no amount to be ceded to SwissRe. Therefore, the amount SwissRe will pay is \( 0 \). ### Conclusion: SwissRe will pay \( \$ 0 \) for the \( \$ 200,000 \) loss because the entire loss is within Trust's retention limit.