# Question: Carolyn is senior vice president of finance and chief actuary

Carolyn is senior vice president of finance and chief actuary for Rock Solid Insurance Company (RSIC). Lonnie is double-majoring in finance and mathematics at State University. Lonnie applied for an internship with Rock Solid, and he is working for the company during the summer before the start of his senior year of college.
Curious to learn what Lonnie knew about insurance company financial statements and ratemaking, Carolyn prepared a quiz for Lonnie to take on his first day on the job. See if you can help Lonnie answer these questions.
1. At year-end last year, Rock Solid had total liabilities of \$640 million and total assets of \$900 million.
What was the company's policyholders' surplus?
2. Explain how it is possible for Rock Solid to have
\$500 million in written premiums last year and \$505 million in earned premiums last year.
3. Rock Solid's net underwriting result last year was a \$540,000 loss. Explain how it is possible that Rock Solid was required to pay income taxes.
4. Rock Solid provides collision coverage for one year on 50,000 autos located in a specific territory within the state. During the one-year period, the company expects to pay \$10 million in incurred losses and loss-adjustment expenses for these 50,000 autos. Based on this information, what is the pure premium?
5. The pure premium per unit of personal liability insurance for one group of prospective purchasers is \$300. If Rock Solid wants to allow for a 40 percent expense ratio for this line of coverage, what gross rate per unit of coverage should be charged?

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