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?

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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.
SwissRe will pay \$0 for the \$200,000 loss because it is within Trust's \$200,000 retention limit.

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?

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