Risk Mgmt + Ins: Exam 2: Math Only

1. Comparative Negligence: $50,000 damages; plaintiff 20% at fault. Recovery?

$50,000 × (1 − 0.20) = $40,000

2. Coinsurance: Home $200,000; 80% requirement; $120,000 insured; $40,000 loss. Payment?

Required = $160,000; Ratio = 120,000 ÷ 160,000 = 75%; Payment = $30,000

3. Pro-Rata Liability: A covers $100,000; B covers $300,000; loss $40,000. Shares?

A pays $10,000; B pays $30,000

4. ACV: Replacement cost $30,000; depreciation $8,000. ACV?

$30,000 − $8,000 = $22,000

5. Annuity: $100,000 investment; $1,000 monthly; 10 years. Expected return and exclusion ratio?

Expected return = $120,000; exclusion ratio = $100,000 ÷ $120,000 = 83.33%

6. IRA Tax Savings: $4,000 deductible contribution; 25% tax rate. Savings?

$4,000 × 25% = $1,000

7. Earned Premium: Written $200,000; beginning unearned $50,000; ending unearned $30,000. Earned?

$200,000 + $50,000 − $30,000 = $220,000

8. Pure Premium: Losses $100,000; LAE $20,000; 400 cars. Pure premium per car?

($100,000 + $20,000) ÷ 400 = $300 per car

9. Gross Rate: Pure premium $200; loading 25%. Gross rate?

$200 ÷ (1 − 0.25) = $266.67

10. Loss Ratio Method: Actual 80%; expected 60%. Rate increase?

(80% − 60%) ÷ 60% = 33.33% increase

11. Premium: Rate $250; 40 exposure units. Total premium?

$250 × 40 = $10,000

12. Loss Ratio: Incurred losses $300,000; earned premiums $500,000. Ratio?

$300,000 ÷ $500,000 = 60%

13. Expense Ratio: Underwriting expenses $100,000; written premiums $400,000. Ratio?

$100,000 ÷ $400,000 = 25%

14. Combined Ratio: Loss ratio 70%; expense ratio 35%. Ratio and result?

70% + 35% = 105%; underwriting loss

15. Investment Income Ratio: Investment income $20,000; earned premiums $250,000. Ratio?

$20,000 ÷ $250,000 = 8%

16. Operating Ratio: Combined 105%; investment income ratio 10%. Ratio and result?

105% − 10% = 95%; overall operating profit